Theorem reximia 2600

Description: Inference quantifying both antecedent and consequent. (Contributed by NM, 10-Feb-1997.)

Hypothesis

Ref	Expression
reximia.1	|- ( x e. A -> ( ph -> ps ) )

Assertion

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

Proof of Theorem reximia

Step	Hyp	Ref	Expression
1		rexim 2599	. 2 |- ( A. x e. A ( ph -> ps ) -> ( E. x e. A ph -> E. x e. A ps ) )
2		reximia.1	. 2 |- ( x e. A -> ( ph -> ps ) )
3	1, 2	mprg 2562	1 |- ( E. x e. A ph -> E. x e. A ps )

Syntax hints:   -> wi 4   e. wcel 2175   E.wrex 2484

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-5 1469  ax-gen 1471  ax-ie1 1515  ax-ie2 1516  ax-4 1532  ax-ial 1556

This theorem depends on definitions:  df-bi 117  df-ral 2488  df-rex 2489

This theorem is referenced by:  reximi  2602  iunpw  4526  nsmallnqq  7524  1idprl  7702  1idpru  7703  qmulz  9743  zq  9746  caubnd2  11370  sin0pilem1  15195