Theorem reximi2 2721

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

Hypothesis

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

Assertion

Ref	Expression
reximi2	|- (E.x e. A ph -> E.x e. B ps)

Proof of Theorem reximi2

Step	Hyp	Ref	Expression
1		reximi2.1	. . 3 |- ((x e. A /\ ph) -> (x e. B /\ ps))
2	1	eximi 1576	. 2 |- (E.x(x e. A /\ ph) -> E.x(x e. B /\ ps))
3		df-rex 2621	. 2 |- (E.x e. A ph <-> E.x(x e. A /\ ph))
4		df-rex 2621	. 2 |- (E.x e. B ps <-> E.x(x e. B /\ ps))
5	2, 3, 4	3imtr4i 257	1 |- (E.x e. A ph -> E.x e. B ps)

Syntax hints:   -> wi 4   /\ wa 358  E.wex 1541   e. wcel 1710  E.wrex 2616

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557

This theorem depends on definitions:  df-bi 177  df-ex 1542  df-rex 2621

This theorem is referenced by: (None)