Theorem ralimdv

Description: Deduction quantifying both antecedent and consequent, based on Theorem 19.20 of Margaris p. 90 ( alim ). (Contributed by NM, 8-Oct-2003)

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

Proof

Step	Hyp	Ref	Expression
1		ralimdv.1	|- ( ph -> ( ps -> ch ) )
2	1	adantr	|- ( ( ph /\ x e. A ) -> ( ps -> ch ) )
3	2	ralimdva	|- ( ph -> ( A. x e. A ps -> A. x e. A ch ) )