Charles Anthony Brown, a pro se Michigan prisoner, appeals a district court judgment denying his petition for a writ of habeas corpus filed under 28 U.S.C. § 2254. This case has been referred to a panel of the court pursuant to Rule 34(j)(l), Rules of the Sixth Circuit. Upon examination, this panel unanimously agrees that oral argument is not needed. Fed. R.App. P. 34(a).
A judge found Brown guilty on October 30, 1995, after a bench trial, of armed robbery and felony firearm. Brown was sentenced on December 7, 1995, to 25-50 years for the armed robbery count, and a consecutive two years for the felony firearm count. The sentences were imposed to run concurrently with other state sentences he was serving. The Michigan Court of Appeals summarily denied Brown’s delayed application for leave to appeal on May 8, 1997, and the Michigan Supreme Court subsequently denied Brown’s delayed application for leave to appeal.
In his federal habeas corpus petition, Brown presented three grounds for relief: (1) he was denied his due process right to a fair trial before an impartial fact-finder where the judge presiding at his bench trial also presided at a pretrial evidentiary hearing in which the judge was exposed to unfairly prejudicial information and where the judge evidenced on the record a preconceived notion about Brown’s guilt; (2) Brown was denied the effective assistance of counsel where his appointed trial counsel waived a jury trial and then failed to revoke the waiver when it became clear that the judge could not sit as an impartial fact-finder and after stand-in defense counsel told the judge that Brown could not attend a pretrial hearing because he was in another court regarding a series of robberies; and (3) his convictions were not supported by evidence sufficient to prove guilt beyond a reasonable doubt.
In a report filed on January 26, 2000, a magistrate judge recommended that Brown’s petition be denied. Brown filed timely objections to the recommended disposition of grounds one and two, and argued that the magistrate judge erred by finding that the Michigan courts’ summary denials of his appeal were based upon a state procedural bar. The district court *156overruled Brown’s objections, adopted the magistrate judge’s report, and dismissed Brown’s § 2254 petition in a memorandum opinion and order filed on May 31 and entered on June 1, 2000. A separate judgment was entered the same day. This court granted a certificate of appealability as to Brown’s grounds for relief asserting impartial fact-finder and ineffective assistance of trial counsel for failing to revoke his waiver of a jury trial. On appeal, Brown continues to argue the merits of these two issues.
Upon review, we affirm the district court’s judgment, in part for reasons other than those stated by the district court. See Brown v. Tidwell, 169 F.3d 330, 332 (6th Cir.1999). This court reviews de novo a district court’s disposition of a habeas corpus petition. Doan v. Brigano, 237 F.3d 722, 729 (6th Cir.2001); Harris v. Stovall, 212 F.3d 940, 942 (6th Cir.2000), cert. denied, — U.S.-, 121 S.Ct. 1415, 149 L.Ed.2d 356, 2001 WL 285959 (Mar. 26, 2001) (No. 00-8185). Pursuant to § 2254, relief may not be granted with respect to any claim adjudicated on the merits in state court unless the adjudication:
(1) resulted in a decision that was contrary to, or involved an unreasonable application of, clearly established Federal law, as determined by the Supreme Court of the United States; or
(2) resulted in a decision that was based on an unreasonable determination of the facts in light of the evidence presented in the State court proceeding.
28 U.S.C. § 2254(d)(l)-(2); Doan, 237 F.3d at 729.
In this case, there is no reasoned state court opinion. Both the Michigan Court of Appeals and the Michigan Supreme Court issued summary orders denying relief. In such a case, the federal court must “conduct an independent review of the record and applicable law to determine whether the state court decision is contrary to federal law, unreasonably applies clearly established law, or is based on an unreasonable determination of the facts in light of the evidence presented.” Harris, 212 F.3d at 943. “Where a state court decides a constitutional issue by form order or without extended discussion, a habeas court should then focus on the result of the state court’s decision, applying the standard articulated above.” Id. at 943 n. 1.
The district court found that federal habeas review on the merits of Brown’s first ground for relief was barred because of his procedural default in the state courts. It is well-settled that “[a] petitioner procedurally defaults claims for habeas relief if the petitioner has not presented those claims to the state courts in accordance with the state’s procedural rules.” Simpson v. Jones, 238 F.3d 399, 406 (6th Cir.2000). “In order for the doctrine to apply, however, the last state court rendering a judgment in the case must have based its judgment on the procedural default.” Id. “A procedural default analysis, then, is two-fold: the federal court must determine if a petitioner failed to comply with a state procedural rule; and it also must analyze whether the state court based its decision on the state procedural rule.” Id. (emphasis added). If both of these conditions are present, the federal court may not review those habeas claims on the merits unless the prisoner can demonstrate either cause for his noncompliance and actual prejudice, or a fundamental miscarriage of justice. Id.
In finding that Brown’s first issue was procedurally defaulted in the state courts, the district court noted that, in his brief to the Michigan Court of Appeals, Brown admitted that he did not properly *157preserve the issue for review. The federal court, however, is not directed to look to the prisoner’s brief on appeal to determine default, but to the state court’s decision. In this case, neither the Michigan Court of Appeals nor the Michigan Supreme Court issued a reasoned opinion on Brown’s appeal. Thus, despite any admitted failure to follow a procedural rule, it cannot be said that the state courts clearly rested upon the procedural default as an independent ground to deny Brown’s appeal. In fact, the court of appeals’ decision expressly states that Brown’s “delayed application for leave to appeal is denied for lack of merit in the grounds presented.” (Emphasis added). The federal courts cannot ignore this language, even in a standard order, and we conclude that the district court erred in finding Brown’s first ground for relief barred from § 2254 review on the merits because of procedural default.
Nonetheless, we affirm the district court’s judgment because we conclude that Brown’s issue relating to the alleged denial of an impartial fact-finder may readily be dismissed on the merits on the record before this court.
This court recently considered an allegation of judicial bias in a § 2254 case. “Because judicial bias infects the entire trial process it is not subject to harmless error review.” Maurino v. Johnson, 210 F.3d 638, 645 (6th Cir.), cert. denied, — U.S. -, 121 S.Ct. 427, 148 L.Ed.2d 435 (2000); see also Chapman v. California, 386 U.S. 18, 23, 87 S.Ct. 824, 17 L.Ed.2d 705 & n .8 (1967). “Instead, the court is required to assess whether the actions of the judge rose to the level of judicial bias. If the court determines that the actions resulted in a constitutional violation, then the court is required to overturn the state court decision. In reviewing claims of judicial bias, this court is guided by the decision in Liteky v. United States, 510 U.S. 540, 114 S.Ct. 1147, 127 L.Ed.2d 474 (1994).” Maurino, 210 F.3d at 645.
The only disqualifying circumstance cited by Brown is the judge’s personal knowledge of the other robberies for which he was charged or convicted. This knowledge, however, is insufficient to require the trial judge’s recusal under Liteky. “[0]pinions formed by the judge on the basis of facts introduced or events occurring in the course of the current proceedings, or of prior proceedings, do not constitute a basis for a bias or partiality motion unless they display a deep-seated favoritism or antagonism that would make fair judgment impossible.” Liteky, 510 U.S. at 555, 114 S.Ct. 1147. A bench trial judge is presumed to have considered only the relevant and admissible evidence in reaching his decision. United States v. Foley, 871 F.2d 235, 240 (1st Cir.1989); United States v. Joseph, 781 F.2d 549, 552 (6th Cir.1986); United States ex rel. Placek v. Illinois, 546 F.2d 1298, 1304 (7th Cir.1976). Brown has presented no evidence to overcome that presumption.
Nor is Brown entitled to habeas relief on the basis of his ineffective assistance of counsel claim. This claim is based upon counsel’s failure to withdraw Brown’s waiver of a jury trial after the judge was exposed to the information regarding his other charged robberies. To establish ineffective assistance of counsel, a petitioner must show that counsel’s performance was deficient and that this deficient performance rendered his trial unfair and the result unreliable. Strickland v. Washington, 466 U.S. 668, 687, 104 S.Ct. 2052, 80 L.Ed.2d 674 (1984).
The district court properly concluded that the result reached by the state courts—that counsel was not constitutionally ineffective—was in accordance with Strickland. Brown personally expressed his desire to continue with the waiver of a *158jury trial, even after the judge gave him the opportunity to withdraw it. That opportunity came during the motion hearing at which the judge acknowledged his awareness of Brown’s other charges and sentence. Brown may therefore not now complain that his attorney did not withdraw the waiver. Furthermore, even if it is assumed that counsel should have advised Brown to withdraw the waiver, Brown has failed to demonstrate prejudice to his defense, i.e., that the result of a jury trial would have been different. Finally, to the extent Brown argues that counsel should have filed a motion for the judge to disqualify himself, it would likely have been denied for the reasons already discussed.
Accordingly, the district court’s judgment, entered on June 1, 2000, is affirmed. Rule 34(j)(2)(C), Rules of the Sixth Circuit.