Theorem ralimdva

Description: Deduction quantifying both antecedent and consequent, based on Theorem 19.20 of Margaris p. 90. (Contributed by NM, 22-May-1999) Reduce dependencies on axioms. (Revised by Wolf Lammen, 5-Dec-2019)

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

Proof

Step	Hyp	Ref	Expression
1		ralimdva.1	|- ( ( ph /\ x e. A ) -> ( ps -> ch ) )
2	1	ex	|- ( ph -> ( x e. A -> ( ps -> ch ) ) )
3	2	a2d	|- ( ph -> ( ( x e. A -> ps ) -> ( x e. A -> ch ) ) )
4	3	ralimdv2	|- ( ph -> ( A. x e. A ps -> A. x e. A ch ) )