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 e. _V
Assertion	abrexex	|- { y | E. x e. A y = B } e. _V

Proof

Step	Hyp	Ref	Expression
1		abrexex.1	|- A e. _V
2		abrexexg	|- ( A e. _V -> { y | E. x e. A y = B } e. _V )
3	1 2	ax-mp	|- { y | E. x e. A y = B } e. _V