Theorem resexg

Description: The restriction of a set is a set. (Contributed by NM, 28-Mar-1998) (Proof shortened by Andrew Salmon, 27-Aug-2011)

	Ref	Expression
Assertion	resexg	$$⊢A\in V\to {A\upharpoonright }_B\in \mathrm{V}$$

Proof

Step	Hyp	Ref	Expression
1		resss	$$⊢{A\upharpoonright }_B\subseteq A$$
2		ssexg	$$⊢\left({A\upharpoonright }_B\subseteq A\wedge A\in V\right)\to {A\upharpoonright }_B\in \mathrm{V}$$
3	1 2	mpan	$$⊢A\in V\to {A\upharpoonright }_B\in \mathrm{V}$$