Theorem rexlimdv3a

Description: Inference from Theorem 19.23 of Margaris p. 90 (restricted quantifier version). Frequently-used variant of rexlimdv . (Contributed by NM, 7-Jun-2015)

	Ref	Expression
Hypothesis	rexlimdv3a.1	|- ( ( ph /\ x e. A /\ ps ) -> ch )
Assertion	rexlimdv3a	|- ( ph -> ( E. x e. A ps -> ch ) )

Proof

Step	Hyp	Ref	Expression
1		rexlimdv3a.1	|- ( ( ph /\ x e. A /\ ps ) -> ch )
2	1	3exp	|- ( ph -> ( x e. A -> ( ps -> ch ) ) )
3	2	rexlimdv	|- ( ph -> ( E. x e. A ps -> ch ) )