Theorem reximia 2582

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 2581	. 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 2544	1 |- ( E. x e. A ph -> E. x e. A ps )

Syntax hints:   -> wi 4   e. wcel 2158   E.wrex 2466

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 1457  ax-gen 1459  ax-ie1 1503  ax-ie2 1504  ax-4 1520  ax-ial 1544

This theorem depends on definitions:  df-bi 117  df-ral 2470  df-rex 2471

This theorem is referenced by:  reximi  2584  iunpw  4492  nsmallnqq  7425  1idprl  7603  1idpru  7604  qmulz  9637  zq  9640  caubnd2  11140  sin0pilem1  14498