Theorem fnresin2

Description: Restriction of a function's domain with an intersection. (Contributed by NM, 9-Aug-1994)

	Ref	Expression
Assertion	fnresin2	$$⊢FFnA\to \left({F\upharpoonright }_{\left(B\cap A\right)}\right)Fn\left(B\cap A\right)$$

Proof

Step	Hyp	Ref	Expression
1		inss2	$$⊢B\cap A\subseteq A$$
2		fnssres	$$⊢\left(FFnA\wedge B\cap A\subseteq A\right)\to \left({F\upharpoonright }_{\left(B\cap A\right)}\right)Fn\left(B\cap A\right)$$
3	1 2	mpan2	$$⊢FFnA\to \left({F\upharpoonright }_{\left(B\cap A\right)}\right)Fn\left(B\cap A\right)$$