Theorem ralrimdva

Description: Inference from Theorem 19.21 of Margaris p. 90. (Restricted quantifier version.) (Contributed by NM, 2-Feb-2008) (Proof shortened by Wolf Lammen, 28-Dec-2019)

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

Proof

Step	Hyp	Ref	Expression
1		ralrimdva.1	|- ( ( ph /\ x e. A ) -> ( ps -> ch ) )
2	1	expimpd	|- ( ph -> ( ( x e. A /\ ps ) -> ch ) )
3	2	expcomd	|- ( ph -> ( ps -> ( x e. A -> ch ) ) )
4	3	ralrimdv	|- ( ph -> ( ps -> A. x e. A ch ) )