Metamath Proof Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  MPE Home  >  Th. List  >  exsimpr Structured version   Visualization version   GIF version

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
 Copyright terms: Public domain W3C validator