Theorem fssresd

Description: Restriction of a function with a subclass of its domain, deduction form. (Contributed by Glauco Siliprandi, 11-Dec-2019)

	Ref	Expression
Hypotheses	fssresd.1	|- ( ph -> F : A --> B )
	fssresd.2	|- ( ph -> C C_ A )
Assertion	fssresd	|- ( ph -> ( F |` C ) : C --> B )

Proof

Step	Hyp	Ref	Expression
1		fssresd.1	|- ( ph -> F : A --> B )
2		fssresd.2	|- ( ph -> C C_ A )
3		fssres	|- ( ( F : A --> B /\ C C_ A ) -> ( F |` C ) : C --> B )
4	1 2 3	syl2anc	|- ( ph -> ( F |` C ) : C --> B )