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Theorem exsimpr 1833
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 1798 1 (∃𝑥(𝜑𝜓) → ∃𝑥𝜓)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 387  wex 1743
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1759  ax-4 1773
This theorem depends on definitions:  df-bi 199  df-an 388  df-ex 1744
This theorem is referenced by:  19.40  1850  spsbeOLDOLD  2432  spsbeALT  2517  rexex  3180  ceqsexv2d  3456  imassrn  5778  fv3  6514  finacn  9268  dfac4  9340  kmlem2  9369  ac6c5  9700  ac6s3  9705  ac6s5  9709  bj-finsumval0  34067  mptsnunlem  34098  topdifinffinlem  34107  heiborlem3  34570  ac6s3f  34930  moantr  35099
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