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Theorem exsimpr 1795
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 (∃𝑥(𝜑𝜓) → ∃𝑥𝜓)

Proof of Theorem exsimpr
StepHypRef Expression
1 simpr 477 . 2 ((𝜑𝜓) → 𝜓)
21eximi 1759 1 (∃𝑥(𝜑𝜓) → ∃𝑥𝜓)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 384  wex 1701
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1719  ax-4 1734
This theorem depends on definitions:  df-bi 197  df-an 386  df-ex 1702
This theorem is referenced by:  19.40  1796  spsbe  1886  rexex  3001  ceqsexv2d  3234  imassrn  5440  fv3  6164  finacn  8818  dfac4  8890  kmlem2  8918  ac6c5  9249  ac6s3  9254  ac6s5  9258  bj-finsumval0  32772  mptsnunlem  32809  topdifinffinlem  32819  heiborlem3  33230  ac6s3f  33597
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