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Theorem exsimpr 1872
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 485 . 2 ((𝜑𝜓) → 𝜓)
21eximi 1837 1 (∃𝑥(𝜑𝜓) → ∃𝑥𝜓)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 396  wex 1781
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811
This theorem depends on definitions:  df-bi 206  df-an 397  df-ex 1782
This theorem is referenced by:  19.40  1889  elex2  2816  rexex  3079  ceqsexv2d  3497  imassrn  6024  fv3  6860  finacn  9986  dfac4  10058  kmlem2  10087  ac6c5  10418  ac6s3  10423  ac6s5  10427  bj-finsumval0  35756  mptsnunlem  35809  topdifinffinlem  35818  heiborlem3  36272  ac6s3f  36630  moantr  36825
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