Theorem reximdv2

Description: Deduction quantifying both antecedent and consequent, based on Theorem 19.22 of Margaris p. 90. (Contributed by NM, 17-Sep-2003)

	Ref	Expression
Hypothesis	reximdv2.1	|- ( ph -> ( ( x e. A /\ ps ) -> ( x e. B /\ ch ) ) )
Assertion	reximdv2	|- ( ph -> ( E. x e. A ps -> E. x e. B ch ) )

Proof

Step	Hyp	Ref	Expression
1		reximdv2.1	|- ( ph -> ( ( x e. A /\ ps ) -> ( x e. B /\ ch ) ) )
2	1	eximdv	|- ( ph -> ( E. x ( x e. A /\ ps ) -> E. x ( x e. B /\ ch ) ) )
3		df-rex	|- ( E. x e. A ps <-> E. x ( x e. A /\ ps ) )
4		df-rex	|- ( E. x e. B ch <-> E. x ( x e. B /\ ch ) )
5	2 3 4	3imtr4g	|- ( ph -> ( E. x e. A ps -> E. x e. B ch ) )