Theorem rexlimdvva

Description: Inference from Theorem 19.23 of Margaris p. 90. (Restricted quantifier version.) (Contributed by NM, 18-Jun-2014)

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

Proof

Step	Hyp	Ref	Expression
1		rexlimdvva.1	|- ( ( ph /\ ( x e. A /\ y e. B ) ) -> ( ps -> ch ) )
2	1	ex	|- ( ph -> ( ( x e. A /\ y e. B ) -> ( ps -> ch ) ) )
3	2	rexlimdvv	|- ( ph -> ( E. x e. A E. y e. B ps -> ch ) )