Theorem elab2

Description: Membership in a class abstraction, using implicit substitution. (Contributed by NM, 13-Sep-1995)

	Ref	Expression
Hypotheses	elab2.1	|- A e. _V
	elab2.2	|- ( x = A -> ( ph <-> ps ) )
	elab2.3	|- B = { x | ph }
Assertion	elab2	|- ( A e. B <-> ps )

Proof

Step	Hyp	Ref	Expression
1		elab2.1	|- A e. _V
2		elab2.2	|- ( x = A -> ( ph <-> ps ) )
3		elab2.3	|- B = { x | ph }
4	2 3	elab2g	|- ( A e. _V -> ( A e. B <-> ps ) )
5	1 4	ax-mp	|- ( A e. B <-> ps )