Theorem ceqsexv

Description: Elimination of an existential quantifier, using implicit substitution. (Contributed by NM, 2-Mar-1995)

	Ref	Expression
Hypotheses	ceqsexv.1	|- A e. _V
	ceqsexv.2	|- ( x = A -> ( ph <-> ps ) )
Assertion	ceqsexv	|- ( E. x ( x = A /\ ph ) <-> ps )

Proof

Step	Hyp	Ref	Expression
1		ceqsexv.1	|- A e. _V
2		ceqsexv.2	|- ( x = A -> ( ph <-> ps ) )
3		nfv	|- F/ x ps
4	3 1 2	ceqsex	|- ( E. x ( x = A /\ ph ) <-> ps )