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Theorem exsimpr 1738
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 468 . 2  |-  ( (
ph  /\  ps )  ->  ps )
21eximi 1715 1  |-  ( E. x ( ph  /\  ps )  ->  E. x ps )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4    /\ wa 376   E.wex 1671
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1677  ax-4 1690
This theorem depends on definitions:  df-bi 190  df-an 378  df-ex 1672
This theorem is referenced by:  19.40  1739  spsbe  1809  rexex  2843  ceqsexv2d  3071  imassrn  5185  fv3  5892  finacn  8499  dfac4  8571  kmlem2  8599  ac6c5  8930  ac6s3  8935  ac6s5  8939  bj-finsumval0  31772  mptsnunlem  31810  topdifinffinlem  31820  heiborlem3  32209  ac6s3f  32478
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