Theorem rexlimdvv

Description: Inference from Theorem 19.23 of Margaris p. 90. (Restricted quantifier version.) (Contributed by NM, 22-Jul-2004)

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

Proof

Step	Hyp	Ref	Expression
1		rexlimdvv.1	|- ( ph -> ( ( x e. A /\ y e. B ) -> ( ps -> ch ) ) )
2	1	expdimp	|- ( ( ph /\ x e. A ) -> ( y e. B -> ( ps -> ch ) ) )
3	2	rexlimdv	|- ( ( ph /\ x e. A ) -> ( E. y e. B ps -> ch ) )
4	3	rexlimdva	|- ( ph -> ( E. x e. A E. y e. B ps -> ch ) )