Theorem resexd

Description: The restriction of a set is a set. (Contributed by Glauco Siliprandi, 23-Oct-2021)

	Ref	Expression
Hypothesis	resexd.1	$$⊢\phi \to A\in V$$
Assertion	resexd	$$⊢\phi \to {A\upharpoonright }_B\in \mathrm{V}$$

Proof

Step	Hyp	Ref	Expression
1		resexd.1	$$⊢\phi \to A\in V$$
2		resexg	$$⊢A\in V\to {A\upharpoonright }_B\in \mathrm{V}$$
3	1 2	syl	$$⊢\phi \to {A\upharpoonright }_B\in \mathrm{V}$$