Theorem bj-abvALT

Description: Alternate version of bj-abv ; shorter but uses ax-8 . (Contributed by BJ, 24-Jul-2019) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Assertion	bj-abvALT	|- ( A. x ph -> { x | ph } = _V )

Proof

Step	Hyp	Ref	Expression
1		ax-5	|- ( A. x ph -> A. y A. x ph )
2		vexwt	|- ( A. x ph -> y e. { x | ph } )
3	1 2	alrimih	|- ( A. x ph -> A. y y e. { x | ph } )
4		eqv	|- ( { x | ph } = _V <-> A. y y e. { x | ph } )
5	3 4	sylibr	|- ( A. x ph -> { x | ph } = _V )