MEMORANDUM

A California jury convicted Miguel Garcia, Jr. of first-degree murder and unlawful firearm possession. After the district court denied his federal habeas petition, we granted him a certificate of appealability (“COA”) on three issues. 28 U.S.C. § 2253 . We consider them in turn, and then address his uncertified issue.

I

Garcia’s trial counsel stipulated to, and did not request a limiting instruction in connection with, certain testimony by prosecution witness Robert Zapien. On redirect examination Zapien stated that, while the two men were cellmates, Garcia had callously recounted having earlier shot a child. Garcia asserts that this violated his Sixth Amendment right to effective assistance of counsel and his right to due process of law.

A

To prevail on an ineffective assistance claim, Garcia “must demonstrate a reasonable probability that, but for coun sel’s unprofessional errors, the result of the proceeding would have been different.” Runningeagle v. Ryan, 686 F.3d 758, 775 (9th Cir.2012) (citation and internal quotation marks omitted). Because AEDPA applies, that “likelihood of a different result must be substantial, not just conceivable.” Harrington v. Richter, — U.S. -, 131 S.Ct. 770, 792 , 178 L.Ed.2d 624 (2011). The jury was instructed to view Zapien’s testimony “with caution and close scrutiny.” There was substantial other evidence of Garcia’s guilt, including statements by another witness to authorities that Garcia confessed to the killing. Had the challenged testimony been excluded, there is not a substantial probability that the verdict would have been different. See Ben-Sholom v. Ayers, 674 F.3d 1095, 1101-03 (9th Cir.2012).

B

Garcia’s claim that Zapien’s testimony was impermissible character evidence and inflammatory such that it violates the Due Process Clause also fails. In Jammal v. Van de Kamp, we reiterated that the “issue is not whether introduction of [the evidence] violated state law evidentiary principles, but whether the trial court committed an error which rendered the trial so arbitrary and fundamentally unfair that it violated federal due process.” 926 F.2d 918, 920 (9th Cir.1991) (alteration in original) (quoting Reiger v. Christensen, 789 F.2d 1425, 1430 (9th Cir.1986)). As the state court found, the prosecution introduced the challenged testimony to rehabilitate Zapien, whom Garcia had impeached as having a self-interested motive for testifying. Garcia has not shown that the state court’s resolution of this issue “involved an unreasonable application of,” or “was contrary to” federal law clearly established in the holdings of the Supreme Court. Harrington v. Richter, — U.S. -, 131 S.Ct. 770, 785 , 178 L.Ed.2d 624 (2011) (quoting 28 U.S.C. § 2254 (d)(1)).

II

In his third certified issue, Garcia claims that the failure of the trial court to administer a California jury instruction on accomplice testimony abridged his due process rights. He cannot demonstrate that this alleged error, held harmless by the state court, “so infected the entire trial that the resulting conviction violates due process.” Clark v. Brown, 450 F.3d 898, 904 (9th Cir.2006) (quoting Estelle v. McGuire, 502 U.S. 62, 72 , 112 S.Ct. 475 , 116 L.Ed.2d 385 (1991)).

III

We decline to expand the COA to include whether the exclusion of unspecified evidence that a third-party had a motive to commit the murder violated Garcia’s constitutional right to present a complete defense. See Holmes v. South Carolina, 547 U.S. 319, 324-25 , 126 S.Ct. 1727 , 164 L.Ed.2d 503 (2006). The application of the California evidentiary rule calling for an offer of proof to this case neither contradicts “the governing law set forth in Supreme Court cases,” nor “confronts a set of facts materially indistinguishable from those at issue in a decision of the Supreme Court.” Lambert v. Blodgett, 393 F.3d 943, 974 (9th Cir.2004).

AFFIRMED.

This disposition is not appropriate for publication and is not precedent except as provided by 9th Cir. R. 36-3.