—Appeal by the defendant from a judgment of the Supreme Court, Kings County (Feldman, J.), rendered November 27, 1995, convicting him of assault in the first degree, upon a jury verdict, and imposing sentence.

Ordered that the judgment is affirmed.

The trial court did not improvidently exercise its discretion by limiting the defendant’s cross-examination of the victim about collateral, irrelevant matters (see, People v McGriff, 201 AD2d 672).

Since the defendant was convicted of assault in the first degree under Penal Law § 120.10 (3) (depraved indifference assault), the jury never reached the lesser-included offense of assault in the second degree under Penal Law § 120.05 (1) (intent to cause serious physical injury). Therefore, we do not consider whether the more remote lesser-included offense of assault in third degree under Penal Law § 120.00 (1) (intent to cause injury) also should have been submitted (see, People v Johnson, 87 NY2d 357, 361; People v Boettcher, 69 NY2d 174, *463180 [“where a court charges the next lesser included offense of the crime alleged in the indictment, but refuses to charge lesser degrees than that, we have noted that the defendant’s conviction of the crime alleged in the indictment forecloses a challenge to the court’s refusal to charge the remote lesser included offenses”]). Thompson, J. P., Krausman, Goldstein and Luciano, JJ., concur.