Theorem fvresd

Description: The value of a restricted function, deduction version of fvres . (Contributed by Glauco Siliprandi, 8-Apr-2021)

	Ref	Expression
Hypothesis	fvresd.1	$$⊢\phi \to A\in B$$
Assertion	fvresd	$$⊢\phi \to \left({F\upharpoonright }_B\right)\left(A\right)=F\left(A\right)$$

Proof

Step	Hyp	Ref	Expression
1		fvresd.1	$$⊢\phi \to A\in B$$
2		fvres	$$⊢A\in B\to \left({F\upharpoonright }_B\right)\left(A\right)=F\left(A\right)$$
3	1 2	syl	$$⊢\phi \to \left({F\upharpoonright }_B\right)\left(A\right)=F\left(A\right)$$