Theorem reximdvai

Description: Deduction quantifying both antecedent and consequent, based on Theorem 19.22 of Margaris p. 90. (Contributed by NM, 14-Nov-2002) Reduce dependencies on axioms. (Revised by Wolf Lammen, 8-Jan-2020) (Proof shortened by Wolf Lammen, 4-Nov-2024)

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

Proof

Step	Hyp	Ref	Expression
1		reximdvai.1	|- ( ph -> ( x e. A -> ( ps -> ch ) ) )
2	1	imdistand	|- ( ph -> ( ( x e. A /\ ps ) -> ( x e. A /\ ch ) ) )
3	2	reximdv2	|- ( ph -> ( E. x e. A ps -> E. x e. A ch ) )