ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  simp3bi GIF version

Theorem simp3bi 932
Description: Deduce a conjunct from a triple conjunction. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.)
Hypothesis
Ref Expression
3simp1bi.1 (𝜑 ↔ (𝜓𝜒𝜃))
Assertion
Ref Expression
simp3bi (𝜑𝜃)

Proof of Theorem simp3bi
StepHypRef Expression
1 3simp1bi.1 . . 3 (𝜑 ↔ (𝜓𝜒𝜃))
21biimpi 117 . 2 (𝜑 → (𝜓𝜒𝜃))
32simp3d 929 1 (𝜑𝜃)
Colors of variables: wff set class
Syntax hints:  wi 4  wb 102  w3a 896
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105
This theorem depends on definitions:  df-bi 114  df-3an 898
This theorem is referenced by:  limuni  4160  smores2  5939  ersym  6148  ertr  6151  eluzle  8580
  Copyright terms: Public domain W3C validator