Theorem fnssres

Description: Restriction of a function with a subclass of its domain. (Contributed by NM, 2-Aug-1994)

	Ref	Expression
Assertion	fnssres	$$⊢\left(FFnA\wedge B\subseteq A\right)\to \left({F\upharpoonright }_B\right)FnB$$

Proof

Step	Hyp	Ref	Expression
1		fnssresb	$$⊢FFnA\to \left(\left({F\upharpoonright }_B\right)FnB\leftrightarrow B\subseteq A\right)$$
2	1	biimpar	$$⊢\left(FFnA\wedge B\subseteq A\right)\to \left({F\upharpoonright }_B\right)FnB$$