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Theorem reximia 2468
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
StepHypRef Expression
1 rexim 2467 . 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 ) )
31, 2mprg 2432 1  |-  ( E. x  e.  A  ph  ->  E. x  e.  A  ps )
Colors of variables: wff set class
Syntax hints:    -> wi 4    e. wcel 1438   E.wrex 2360
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-5 1381  ax-gen 1383  ax-ie1 1427  ax-ie2 1428  ax-4 1445  ax-ial 1472
This theorem depends on definitions:  df-bi 115  df-ral 2364  df-rex 2365
This theorem is referenced by:  reximi  2470  iunpw  4302  nsmallnqq  6969  1idprl  7147  1idpru  7148  qmulz  9106  zq  9109  caubnd2  10546
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