Theorem fnssresd

Description: Restriction of a function to a subclass of its domain. (Contributed by Glauco Siliprandi, 5-Feb-2022)

	Ref	Expression
Hypotheses	fnssresd.1	|- ( ph -> F Fn A )
	fnssresd.2	|- ( ph -> B C_ A )
Assertion	fnssresd	|- ( ph -> ( F |` B ) Fn B )

Proof

Step	Hyp	Ref	Expression
1		fnssresd.1	|- ( ph -> F Fn A )
2		fnssresd.2	|- ( ph -> B C_ A )
3		fnssres	|- ( ( F Fn A /\ B C_ A ) -> ( F |` B ) Fn B )
4	1 2 3	syl2anc	|- ( ph -> ( F |` B ) Fn B )