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Theorem exsimpr 1836
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 476 . 2 ((𝜑𝜓) → 𝜓)
21eximi 1802 1 (∃𝑥(𝜑𝜓) → ∃𝑥𝜓)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 383  wex 1744
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1762  ax-4 1777
This theorem depends on definitions:  df-bi 197  df-an 385  df-ex 1745
This theorem is referenced by:  19.40  1837  spsbe  1941  rexex  3031  ceqsexv2d  3274  imassrn  5512  fv3  6244  finacn  8911  dfac4  8983  kmlem2  9011  ac6c5  9342  ac6s3  9347  ac6s5  9351  bj-finsumval0  33277  mptsnunlem  33315  topdifinffinlem  33325  heiborlem3  33742  ac6s3f  34109  moantr  34267
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