Theorem ceqsrexv2

Description: Alternate elimitation of a restricted existential quantifier, using implicit substitution. (Contributed by Scott Fenton, 5-Sep-2017)

	Ref	Expression
Hypothesis	ceqsrexv2.1	|- ( x = A -> ( ph <-> ps ) )
Assertion	ceqsrexv2	|- ( E. x e. B ( x = A /\ ph ) <-> ( A e. B /\ ps ) )

Proof

Step	Hyp	Ref	Expression
1		ceqsrexv2.1	|- ( x = A -> ( ph <-> ps ) )
2	1	ceqsrexbv	|- ( E. x e. B ( x = A /\ ph ) <-> ( A e. B /\ ps ) )