ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  simp1bi GIF version

Theorem simp1bi 954
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
simp1bi (𝜑𝜓)

Proof of Theorem simp1bi
StepHypRef Expression
1 3simp1bi.1 . . 3 (𝜑 ↔ (𝜓𝜒𝜃))
21biimpi 118 . 2 (𝜑 → (𝜓𝜒𝜃))
32simp1d 951 1 (𝜑𝜓)
Colors of variables: wff set class
Syntax hints:  wi 4  wb 103  w3a 920
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104
This theorem depends on definitions:  df-bi 115  df-3an 922
This theorem is referenced by:  limord  4178  smores2  5964  smofvon2dm  5966  smofvon  5969  errel  6203  lincmb01cmp  9171  iccf1o  9172  elfznn0  9277  elfzouz  9308
  Copyright terms: Public domain W3C validator