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

Theorem exsimpr 1873
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 486 . 2 ((𝜑𝜓) → 𝜓)
21eximi 1838 1 (∃𝑥(𝜑𝜓) → ∃𝑥𝜓)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 397  wex 1782
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1798  ax-4 1812
This theorem depends on definitions:  df-bi 206  df-an 398  df-ex 1783
This theorem is referenced by:  19.40  1890  elex2  2813  rexex  3076  ceqsexv2d  3496  imassrn  6025  fv3  6861  finacn  9991  dfac4  10063  kmlem2  10092  ac6c5  10423  ac6s3  10428  ac6s5  10432  bj-finsumval0  35802  mptsnunlem  35855  topdifinffinlem  35864  heiborlem3  36318  ac6s3f  36676  moantr  36871
  Copyright terms: Public domain W3C validator