Theorem abrexex

Description: Existence of a class abstraction of existentially restricted sets. See the comment of abrexexg . See also abrexex2 . (Contributed by NM, 16-Oct-2003) (Proof shortened by Mario Carneiro, 31-Aug-2015)

	Ref	Expression
Hypothesis	abrexex.1	$$⊢A\in \mathrm{V}$$
Assertion	abrexex	$$⊢\left\{y|\exists x\in Ay=B\right\}\in \mathrm{V}$$

Proof

Step	Hyp	Ref	Expression
1		abrexex.1	$$⊢A\in \mathrm{V}$$
2		abrexexg	$$⊢A\in \mathrm{V}\to \left\{y|\exists x\in Ay=B\right\}\in \mathrm{V}$$
3	1 2	ax-mp	$$⊢\left\{y|\exists x\in Ay=B\right\}\in \mathrm{V}$$