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Theorem exsimpr 1646
Description: Simplification of an existentially quantified conjunction. (Contributed by Rodolfo Medina, 25-Sep-2010.) (Proof shortened by Andrew Salmon, 29-Jun-2011.)
Assertion
Ref Expression
exsimpr  |-  ( E. x ( ph  /\  ps )  ->  E. x ps )

Proof of Theorem exsimpr
StepHypRef Expression
1 simpr 461 . 2  |-  ( (
ph  /\  ps )  ->  ps )
21eximi 1626 1  |-  ( E. x ( ph  /\  ps )  ->  E. x ps )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4    /\ wa 369   E.wex 1587
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1592  ax-4 1603
This theorem depends on definitions:  df-bi 185  df-an 371  df-ex 1588
This theorem is referenced by:  19.40  1647  spsbe  1706  euanOLD  2341  rexex  2893  imassrn  5289  fv3  5813  finacn  8332  dfac4  8404  kmlem2  8432  ac6c5  8763  ac6s3  8768  ac6s5  8772  ac6s3f  29132  bj-finsumval0  32922
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