Theorem reximi2

Description: Inference quantifying both antecedent and consequent, based on Theorem 19.22 of Margaris p. 90. (Contributed by NM, 8-Nov-2004)

	Ref	Expression
Hypothesis	reximi2.1	|- ( ( x e. A /\ ph ) -> ( x e. B /\ ps ) )
Assertion	reximi2	|- ( E. x e. A ph -> E. x e. B ps )

Proof

Step	Hyp	Ref	Expression
1		reximi2.1	|- ( ( x e. A /\ ph ) -> ( x e. B /\ ps ) )
2	1	eximi	|- ( E. x ( x e. A /\ ph ) -> E. x ( x e. B /\ ps ) )
3		df-rex	|- ( E. x e. A ph <-> E. x ( x e. A /\ ph ) )
4		df-rex	|- ( E. x e. B ps <-> E. x ( x e. B /\ ps ) )
5	2 3 4	3imtr4i	|- ( E. x e. A ph -> E. x e. B ps )