Theorem rexlimivv

Description: Inference from Theorem 19.23 of Margaris p. 90 (restricted quantifier version). (Contributed by NM, 17-Feb-2004)

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

Proof

Step	Hyp	Ref	Expression
1		rexlimivv.1	|- ( ( x e. A /\ y e. B ) -> ( ph -> ps ) )
2	1	rexlimdva	|- ( x e. A -> ( E. y e. B ph -> ps ) )
3	2	rexlimiv	|- ( E. x e. A E. y e. B ph -> ps )