Theorem elrab3

Description: Membership in a restricted class abstraction, using implicit substitution. (Contributed by NM, 5-Oct-2006)

	Ref	Expression
Hypothesis	elrab.1	|- ( x = A -> ( ph <-> ps ) )
Assertion	elrab3	|- ( A e. B -> ( A e. { x e. B | ph } <-> ps ) )

Proof

Step	Hyp	Ref	Expression
1		elrab.1	|- ( x = A -> ( ph <-> ps ) )
2	1	elrab	|- ( A e. { x e. B | ph } <-> ( A e. B /\ ps ) )
3	2	baib	|- ( A e. B -> ( A e. { x e. B | ph } <-> ps ) )