Theorem spcev

Description: Existential specialization, using implicit substitution. (Contributed by NM, 31-Dec-1993) (Proof shortened by Eric Schmidt, 22-Dec-2006)

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

Proof

Step	Hyp	Ref	Expression
1		spcv.1	|- A e. _V
2		spcv.2	|- ( x = A -> ( ph <-> ps ) )
3	2	spcegv	|- ( A e. _V -> ( ps -> E. x ph ) )
4	1 3	ax-mp	|- ( ps -> E. x ph )