Theorem ralrimdvv

Description: Inference from Theorem 19.21 of Margaris p. 90. (Restricted quantifier version with double quantification.) (Contributed by NM, 1-Jun-2005)

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

Proof

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