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Theorem exsimpr 1683
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 459 . 2  |-  ( (
ph  /\  ps )  ->  ps )
21eximi 1661 1  |-  ( E. x ( ph  /\  ps )  ->  E. x ps )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4    /\ wa 367   E.wex 1617
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1623  ax-4 1636
This theorem depends on definitions:  df-bi 185  df-an 369  df-ex 1618
This theorem is referenced by:  19.40  1684  spsbe  1748  rexex  2911  imassrn  5336  fv3  5861  finacn  8422  dfac4  8494  kmlem2  8522  ac6c5  8853  ac6s3  8858  ac6s5  8862  ceqsexv2d  27598  heiborlem3  30552  ac6s3f  30822  bj-finsumval0  35082
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