Theorem ralrimdvva

Description: Inference from Theorem 19.21 of Margaris p. 90. (Restricted quantifier version with double quantification.) (Contributed by NM, 2-Feb-2008)

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

Proof

Step	Hyp	Ref	Expression
1		ralrimdvva.1	|- ( ( ph /\ ( x e. A /\ y e. B ) ) -> ( ps -> ch ) )
2	1	ex	|- ( ph -> ( ( x e. A /\ y e. B ) -> ( ps -> ch ) ) )
3	2	com23	|- ( ph -> ( ps -> ( ( x e. A /\ y e. B ) -> ch ) ) )
4	3	ralrimdvv	|- ( ph -> ( ps -> A. x e. A A. y e. B ch ) )