Theorem reximdva

Description: Deduction quantifying both antecedent and consequent, based on Theorem 19.22 of Margaris p. 90. (Contributed by NM, 22-May-1999)

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