*432 Opinion
GRUENDEL. J.The petitioner, Michael A. Edwards, following a grant of certification to appeal by the habeas court, appeals from the judgment of the habeas court denying his amended petition for a writ of habeas corpus. The petitioner claims that the habeas court improperly denied his petition after erroneously finding that his prior habeas counsel had not rendered ineffective assistance. We affirm the judgment of the habeas court.1
The following facts and procedural history are relevant to the resolution of the petitioner’s claim. “During the evening of February 18, 1995, the [petitioner], after closing the family grocery store in which he had been working, approached the victim, [George Wright], on Albany Avenue in Hartford. The two men, who were not friendly, exchanged angry words, and the [petitioner] grabbed the victim’s clothing and held a gun to his head. The [petitioner] then shoved the victim backwards along the sidewalk in front of the store. The victim did not resist, but said ‘no, no, no.’ The [petitioner] then pushed the victim’s head down and shot him in the head. The victim fell to the sidewalk. The bullet entered the left side of the back of the victim’s head, behind the left ear, traveled through the base and right side of the brain and lodged near his right eye. The victim died the following day of injuries sustained as a result of the gunshot wound.” State v. Edwards, 247 Conn. 318, 320-21, 721 A.2d 519 (1998).
After the shooting, the petitioner went to a nearby bar, the Main and Tower Cafe, where he had a conversation with a bouncer named Scott Courtney Davis. The police, approximately one week after the shooting, took *433a signed written statement from Davis, who provided it under the alias, “Isaiah Manuel,” which reads in relevant part: “I followed [the petitioner] into the men’s room .... [The petitioner] went to the sink grabbed a towel and began wetting the towel and wiping down the front of his jacket as he said that he had blood on him because he had just‘popped’ . . . a dude. . . . [The petitioner] looking strange stated that he had popped this dude and wanted to know if I wanted to buy some guns but that one of the guns had a body on it ... . [The petitioner] then stated that if I needed a gun the guns was at [Angela Ford’s] house right now . ...” At a bond reduction hearing, on January 3, 1996, the petitioner’s counsel informed the court and the state’s attorney that Davis had signed the statement under an alias.
At trial, the petitioner testified on his own behalf, stating that he did not hold the gun by the trigger, but only by the barrel, and that while attempting to disarm the victim, the gun went off accidentally. He also testified that he went to the Main and Tower Cafe following the shooting, where he saw Davis, and that he gave the gun used in the shooting to Ford. The state’s attorney, Kevin J. Murphy, cross-examined the petitioner, using the contents of Davis’ statement, to impeach his credibility.2
*434The habeas court set forth the other relevant testimony dining the petitioner’s criminal trial: “Several eyewitnesses testified that they saw the petitioner shoot [the victim] in the back of his head. Although most of the witnesses were either related to [the victim] or friends with [the victim], even the petitioner admitted, during his testimony . . . that [the victim’s] friends and family were in the area when the shooting occurred. Several witnesses also testified that [the victim] would not go into the store where the petitioner worked because he had a ‘beef with the petitioner, which the petitioner also corroborated during his testimony. The petitioner testified that he told the [victim] not to come *435into the store anymore. . . . [T]here was little to no evidence to substantiate the petitioner’s testimony regarding how the shooting occurred. The petitioner and [the victim] were comparable in size. While some of the eyewitnesses saw the petitioner and [the victim] struggle a bit, no one saw the petitioner hook [the victim’s] right arm toward his left side and pull the gun down, as the petitioner testified. . . . [T]he medical examiner testified that [the victim] did not have any abrasions or bruises on his body, apart from a small scrape on his forehead .... Additionally . . . the medical examiner opined, during the state’s rebuttal, that the gunshot wound that he observed in [the victim’s] head could not have been caused by the victim having the gun in his right hand and pointing it to the left side of his head.”
“A jury convicted the [petitioner] ... of murder in violation of General Statutes § 53a-54a, and acquitted him of criminal possession of a firearm in violation of General Statutes § 53a-217 and criminal possession of a pistol in violation of General Statutes § 53a-217c.” State v. Edwards, supra, 247 Conn. 319-20. The trial court sentenced the petitioner to a term of fifty years imprisonment. The petitioner appealed and our Supreme Court affirmed his conviction. Id., 320. Thereafter the petitioner filed a petition for a writ of habeas corpus, claiming, inter alia, that his trial counsel, Donald Cardwell,3 had provided ineffective assistance in violation of the sixth amendment to the United States constitution by failing to advise him about whether to accept aplea agreement, failing to conduct an adequate pretrial investigation and failing to “object to a certain line of questioning” by the prosecutor.4 Edwards v. Commissioner of Correction, 87 Conn. App. 517, 518 and n.1, 865 *436A.2d 1231 (2005). The habeas court denied his petition, which judgment this court affirmed. Id., 518.
The petitioner then brought a second petition for a writ of habeas corpus alleging that his counsel in his first habeas proceeding, Elizabeth Brooks, had rendered ineffective assistance. He argued, inter alia, that his habeas counsel was ineffective because she failed to raise in the petitioner’s first habeas petition that his trial counsel rendered ineffective assistance by failing to object, on the basis of prosecutorial impropriety, to Murphy’s cross-examination of the petitioner. The petitioner argued that, at his criminal trial, Murphy asked questions of him without a good faith basis, which constituted prosecutorial impropriety. Specifically, the petitioner contended that because Davis’ statement was given under an alias, it was inherently unreliable, thereby negating any good faith basis Murphy may have had for asking questions arising from the contents of the statement.
The second habeas court found that Murphy did not engage in prosecutorial impropriety because he did, in fact, have a good faith basis for asking questions based on the contents of Davis’ statement. The court reasoned that Murphy had a good faith basis for asking the questions related to Davis’ statement not only because Murphy testified that he would not have asked the questions without a good faith basis, but because there was evidence to corroborate the facts contained in the statement, Davis testified that he had no animosity toward the petitioner and Davis’ making the statement under an alias did not necessarily lead to the conclusion that the statement was completely false.5 Accordingly, the *437court determined that the petitioner’s prior habeas counsel did not perform deficiently by failing to raise this claim, as it was meritless.
Further, the second habeas court found that the petitioner was not prejudiced by his prior habeas counsel’s failure to raise this claim because the other elements of the state’s case were strong. As the court explained, even if “the trial court struck the line of questioning or prohibited it, there is no reasonable probability that the outcome of the petitioner’s trial would have been different. Thus, this claim would likewise not have succeeded in the prior habeas [matter].” The second habeas court denied the petition for a writ of habeas corpus, but granted certification to appeal, and the petitioner appealed to this court.
“The habeas court is afforded broad discretion in making its factual findings, and those findings will not be disturbed unless they are clearly erroneous. . . . [T]he habeas judge, as the trier of facts, is the sole arbiter of the credibility of witnesses and the weight to be given to their testimony. . . . The application of the habeas court’s factual findings to the pertinent legal standard, however, presents a mixed question of law and fact, which is subject to plenary review.” (Citations omitted; internal quotation marks omitted.) Gaines v. Commissioner of Correction, 306 Conn. 664, 677, 61 A.3d 948 (2012).
“[W]e begin our analysis by setting forth the familiar two part test enunciated by the United States Supreme Court in Strickland v. Washington, [466 U.S. 668, 687, 104 S. Ct. 2052, 80 L. Ed. 2d 674 (1984)]. In Strickland, which applies to claims of ineffective assistance during criminal proceedings generally, the United States *438Supreme Court determined that the claim must be supported by evidence establishing that (1) counsel’s representation fell below an objective standard of reasonableness, and (2) counsel’s deficient performance prejudiced the defense because there was a reasonable probability that the outcome of the proceedings would have been different had it not been for the deficient performance. . . . The first prong is satisfied by proving that counsel made errors so serious that he was not functioning as the counsel guaranteed by the sixth amendment. The second prong is satisfied if it is demonstrated that there exists a reasonable probability that, but for counsel’s unprofessional errors, the result of the proceeding would have been different. . . .
“[When] applied to a claim of ineffective assistance of prior habeas counsel, the Strickland standard requires the petitioner to demonstrate that his prior habeas counsel’s performance was ineffective and that this ineffectiveness prejudiced the petitioner’s prior habeas proceeding. . . . [T]he petitioner will have to prove that . . . the prior habeas counsel, in presenting his claims, was ineffective and that effective representation by habeas counsel establishes a reasonable probability that the habeas court would have found that he was entitled to reversal of the conviction and a new trial .... Therefore, as explained by our Supreme Court in Lozada v. Warden, 223 Conn. 834, 613 A.2d 818 (1992), a petitioner claiming ineffective assistance of habeas counsel on the basis of ineffective assistance of trial counsel must essentially satisfy Strickland twice: he must prove both (1) that his appointed habeas counsel was ineffective, and (2) that his trial counsel was ineffective. . . .
“Furthermore, for any ineffective assistance claim, we also are cognizant that the performance inquiry must be whether counsel’s assistance was reasonable considering all the circumstances. . . . Judicial scrutiny of *439counsel’s performance must be highly deferential. . . . Because of the difficulties inherent in making the evaluation, a court must indulge a strong presumption that counsel's conduct falls within the wide range of reasonable professional assistance; that is, the [petitioner] must overcome the presumption that, under the circumstances, the challenged action might be considered sound trial strategy.” (Citations omitted; emphasis in original; internal quotation marks omitted.) Lapointe v. Commissioner of Correction, 113 Conn. App. 378, 393-95, 966 A.2d 780 (2009).
As the petitioner’s ineffective assistance of counsel claim ultimately rests on his trial counsel’s failure to object on the basis of prosecutorial impropriety to Murphy’s cross-examination of the petitioner using Davis’ statement to impeach his credibility, we also set forth the legal standards for the review of a claim of prosecu-torial impropriety. “In analyzing claims of prosecutorial impropriety, we engage in a two step analytical process. . . . The two steps are separate and distinct. ... We first examine whether prosecutorial impropriety occurred. . . . Second, if an impropriety exists, we then examine whether it deprived the defendant of his due process right to a fair trial. . . . [T]he touchstone of due process analysis in cases of allegedly] [harmful] prosecutorial [impropriety] is the fairness of the trial, and not the culpability of the prosecutor. . . . The issue is whether the prosecutor’s [actions at trial] so infected [it] with unfairness as to make the resulting conviction a denial of due process. ... In determining whether the defendant was denied a fair trial . . . we must view the prosecutor’s [actions] in the context of the entire trial.” (Internal quotation marks omitted.) State v. Souza, 125 Conn. App. 529, 534, 8 A.3d 1131 (2010).
We now turn to the question at the root of the petitioner’s entire claim: whether the petitioner has shown that *440Murphy committed prosecutorial impropriety by asking questions to impeach the petitioner’s credibility based on Davis’ statement. We agree with the habeas court in concluding that the petitioner has failed to make such a showing.
“It is well established that once an accused takes the stand and testifies his credibility is subject to scrutiny and close examination. ... A defendant cannot both take the stand and be immune from impeachment. . . . An accused who testifies subjects himself to the same rules and tests which could by law be applied to other witnesses. . . . [T]he [United States] Supreme Court has noted [in Perry v. Leeke, 488 U.S. 272, 282, 109 S. Ct. 594, 102 L. Ed. 2d 624 (1989)] that when a defendant assumes the role of a witness, the rules that generally apply to other witnesses — rules that serve the truth-seeking function of the trial — are generally applicable to him as well.” (Citations omitted; internal quotation marks omitted.) State v. Alexander, 254 Conn. 290, 297-98, 755 A.2d 868 (2000).
“It is fundamental that for the purpose of impeaching the credibility of his testimony, a witness may be cross-examined as to statements made out of court . . . which contradict those made upon direct examination. . . . This is based on the notion that talking one way on the stand, and another way previously, raises a doubt as to the truthfulness of [those] statements. . . . The purpose of impeachment is to undermine the credibility of a witness so that the trier will disbelieve him and disregard his testimony.” (Citation omitted; internal quotation marks omitted.) State v. Valentine, 240 Conn. 395, 411, 692 A.3d 727 (1997). Yet, “[a] good faith basis on the part of examining counsel as to the truth of the matter contained in questions propounded to a witness on cross-examination is required.” (Internal quotation marks omitted.) State v. Barnes, 232 Conn. 740, 747, 657 A.2d 611 (1995).
*441As the second habeas court explained, the mere fact that Davis’ statement was given to the police under an alias did not necessarily make its contents false, nor did it automatically negate Murphy’s good faith basis for asking impeaching questions. Moreover, there were several ways in which other evidence corroborated the details of Davis’ statement, which supports the habeas court’s conclusion that Murphy did not lack a good faith basis to use Davis’ statement to impeach the petitioner’s credibility. The petitioner admitted that, following the shooting, he went to the Main and Tower Cafe, where Davis was working as a bouncer. This tends to corroborate the description of the time and location in which Davis asserted his conversation with the petitioner occurred. The petitioner also admitted that Davis came into the men’s restroom while the petitioner was washing his face and hands after the shooting. These facts, as the court found, are consistent with Davis’ account that the petitioner made the statements about the gun and the shooting while in the men’s restroom washing his face and hands at the Main and Tower Cafe. Davis’ statement also indicated that the petitioner stated that he had given the gun used in the shooting to Ford, a fact which the petitioner admitted. Davis’ knowledge of the identity of Ford as the person to whom the petitioner had given the gun similarly corroborates the contents of his statement to the police. Given that the contents of Davis’ statement were corroborated by other evidence, the habeas court did not err in finding that Murphy had a good faith basis for asking questions to impeach the petitioner’s credibility based on the statement, despite the fact that Davis provided the statement under an alias. Accordingly, Murphy’s questioning did not constitute prosecutorial impropriety.6
*442Because the petitioner’s claim of prosecutorial impropriety is unavailing, his trial counsel did not render ineffective assistance by failing to object on this basis. It follows then that his prior habeas counsel did not render ineffective assistance by declining to raise a claim that his trial counsel’s assistance was ineffective in failing to object to Murphy’s questioning on the basis of prosecutorial impropriety. Given that the petitioner has not demonstrated that either his trial or prior habeas counsel provided assistance that fell below an objective standard of reasonableness, his claim of ineffective assistance of counsel fails. See Strickland v. Washington, supra, 466 U.S. 668.
The judgment is affirmed.
In this opinion the other judges concurred.
The respondent, the commissioner of correction, contends that the petitioner’s claims are barred by the doctrines of res judicata and collateral estoppel. As we have disposed of the petitioner’s claim on other grounds, we need not address this argument.
The transcript of the relevant portions of Murphy’s cross-examination of the petitioner provides as follows:
“Q. And do you recall when you were at the Main and Tower Cafe, running into a guy named Isaiah Manuel, or Manual?
“A. I don’t know an Isaiah Manual.
“Q. Do you remember running into the bouncer in the bathroom, while you were washing your hands and your coat?
“A. Yes.
“Q. Now, do you remember at the Main and Tower, when you went into the bathroom, and you bumped into the bouncer in the bathroom? Do you remember that?
“A. No. I didn’t bump into him in the bathroom. I went to the bathroom, and I was trying to get — I was looking in the mirror, trying to get — clean my face off, and he came into the — I guess they wanted the money, because I didn’t pay to get in. I just walked in and went straight to the bathroom.
*434“Q. So, you bumped into him while you were washing your face and washing your hands?
“A. He came in — he came in when I was in the bathroom.
“Q. And you were washing your jacket too, weren’t you?
“A. No, I didn’t wash my jacket. If I washed my jacket, there wouldn’t be no blood stains on it, or any stains on it.
“Q. Well, were there stains on it?
“A. Yeah, there were stains on it.
“Q. So, you admit, though, at some point, you’re in the bathroom and so was the bouncer? Is that right?
“A. Yes, he came into the bathroom, yes.
“Q. And you told him you needed to speak with him?
“A. No, I never said — no. Me and Courtney — Courtney’s real name is Courtney Davis, and Courtney Davis, me and him don’t get along. We don’t really talk.
“Q. You’re saying the bouncer’s name is Courtney Davis?
“A. Yes. He’s using a false name, because he’s wanted. And he’s walking around the police department, wanted.
“Q. Do you remember the bouncer helping you clean yourself and got you a towel?
“A. No. That never happened. I was in Main and Tower for less than two minutes. And most of that, I was drinking.
* * *
“Q. Do you remember indicating to the bouncer that you’d just popped a dude and asked him if he wanted to buy a gun?
“A. No. That never happened.
“Q. Do you remember telling him that one of the guns had a body on it?
“A. No. That never happened.
“Q. Do you remember telling him that the gun was at [Ford’s] at the time?
“A. No. I never told him that.”
Cardwell has since passed away.
The petitioner withdrew the claim related to the prosecutor’s questioning. Edwards v. Commissioner of Correction, 87 Conn. App., 517, 518 n.1, 865 A.2d 1231 (2005).
During the second habeas trial, Davis, a felon, testified that he did not tell the police that the petitioner had told him that he had “popped a dude” and that he never told the police that the petitioner had tried to sell him a gun with a “body on it.” The habeas court, however, did not credit this testimony.
During oral argument before this court, the petitioner’s counsel asserted, for the first time, the claim that this factual finding is clearly erroneous. As this claim was not briefed, we deem it abandoned. See Roby v. Connecticut *437General Life Ins. Co., 166 Conn. 396, 398 n.1, 349 A.2d 838 (1974) (claims not briefed deemed abandoned).
As we have not concluded that Murphy’s questioning constituted prosecu-torial impropriety, we need not reach the question of whether his questioning deprived the petitioner of his due process right to a fair trial.