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Theorem exsimpr 1869
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 484 . 2 ((𝜑𝜓) → 𝜓)
21eximi 1835 1 (∃𝑥(𝜑𝜓) → ∃𝑥𝜓)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 395  wex 1779
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1795  ax-4 1809
This theorem depends on definitions:  df-bi 207  df-an 396  df-ex 1780
This theorem is referenced by:  19.40  1886  elex2  2818  rexex  3076  ceqsexv2dOLD  3534  imassrn  6089  fv3  6924  finacn  10090  dfac4  10162  kmlem2  10192  ac6c5  10522  ac6s3  10527  ac6s5  10531  axnulALT2  35107  bj-finsumval0  37286  mptsnunlem  37339  topdifinffinlem  37348  heiborlem3  37820  ac6s3f  38178  moantr  38365
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