ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  exsimpr GIF version

Theorem exsimpr 1618
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 110 . 2 ((𝜑𝜓) → 𝜓)
21eximi 1600 1 (∃𝑥(𝜑𝜓) → ∃𝑥𝜓)
Colors of variables: wff set class
Syntax hints:  wi 4  wa 104  wex 1492
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-5 1447  ax-gen 1449  ax-ie1 1493  ax-ie2 1494  ax-4 1510  ax-ial 1534
This theorem depends on definitions:  df-bi 117
This theorem is referenced by:  cbvexv1  1752  onm  4401  imassrn  4981  eliotaeu  5205  fv3  5538  relelfvdm  5547  nfvres  5548  brtpos2  6251  cc1  7263  omiunct  12439
  Copyright terms: Public domain W3C validator