MEMORANDUM**
William James Mesa appeals the denial of his petition for writ of habeas corpus under 28 U.S.C. § 2254. Mesa claims that ineffective assistance of counsel tainted his Arizona state conviction for first-degree murder and child abuse. He alleges that his attorney’s failure to pursue or utilize potentially exculpatory medical information prejudiced his defense. The Arizona state court of appeals held that Mesa failed to establish ineffective assistance, and the district court denied habeas. We affirm.
As the parties are familiar with the facts of this case, we recite them only as necessary. We review the denial of Mesa’s § 2254 habeas petition de novo. See Alva-rodo v. Hill, 252 F.3d 1066, 1068 (9th Cir.2001).
The Anti-Terrorism and Effective Death Penalty Act of 1996 (AEDPA), 28 U.S.C. § 2241 et seq., narrowly limits federal ha-beas review of state court determinations. Section 2254(d) of the Act dictates that in order to obtain federal habeas relief, a petitioner must demonstrate that the state court’s adjudication of the merits resulted in a decision that was “contrary to” or “an unreasonable application of’ clearly established federal law, or was based on an “unreasonable determination of the facts.” 28 U.S.C. § 2254(d). Here, the Arizona trial and appeal courts applied the standard for ineffective assistance of counsel articulated in Arizona v. Amaya-Ruiz, 166 Ariz. 152, 800 P.2d 1260, 1288 (1990), an Arizona state decision which applied the same “performance” and “prejudice” prongs set forth in Strickland v. Washington, 466 U.S. 668, 690-93, 104 S.Ct. 2052, 80 L.Ed.2d 674 (1984).
A federal court may not issue a writ of habeas corpus “simply because that court concludes in its independent judgment that the relevant state court decision applied clearly established federal law erroneously or incorrectly. Rather, that application must also be unreasonable.” Williams v. Taylor, 529 U.S. 362, 411, 120 S.Ct. 1495, 146 L.Ed.2d 389 (2000). Our review is narrowly limited to determining whether a state court’s ruling contravenes federal law. See Woodford v. Visciotti, — U.S. -, 123 S.Ct. 357, 358, 154 L.Ed.2d 279 (2002)(per curiam), and Early v. Packer, - U.S. -, 123 S.Ct. 362, 364, 154 L.Ed.2d 263 (2002).
*488Under federal law, a petitioner can establish a claim of ineffective assistance of counsel by showing that (1) counsel’s performance was deficient, and (2) the deficient performance prejudiced the outcome of the case. Strickland, 466 U.S. at 687. Where a petitioner cannot show prejudice, the court need not reach the performance prong. Id. at 697. In order to show prejudice, a defendant must establish a “reasonable probability that, but for counsel’s unprofessional errors, the result of the proceeding would have been different.” Id. at 694.
The Arizona appeals court held that it was not reasonably probable that additional medical evidence on short distance falls would have altered the verdicts, as there was overwhelming evidence to support the testimony of the state’s medical experts and the medical journal articles proffered by Mesa could have potentially hurt more than helped his case. Thus, in addition to holding that Mesa’s counsel performed adequately in light of the evidence, the state court determined that Mesa failed to establish prejudice. The district court denied Mesa’s habeas petition on the same grounds. The conclusion of the Arizona court of appeals was not unreasonable, so the federal district court acted properly in declining to grant habeas relief.
The district court’s judgment is AFFIRMED.
This disposition is not appropriate for publication and may not be cited to or by the courts of this circuit except as provided by Ninth Circuit Rule 36-3.