ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  3anan32 GIF version

Theorem 3anan32 958
Description: Convert triple conjunction to conjunction, then commute. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.)
Assertion
Ref Expression
3anan32 ((𝜑𝜓𝜒) ↔ ((𝜑𝜒) ∧ 𝜓))

Proof of Theorem 3anan32
StepHypRef Expression
1 df-3an 949 . 2 ((𝜑𝜓𝜒) ↔ ((𝜑𝜓) ∧ 𝜒))
2 an32 536 . 2 (((𝜑𝜓) ∧ 𝜒) ↔ ((𝜑𝜒) ∧ 𝜓))
31, 2bitri 183 1 ((𝜑𝜓𝜒) ↔ ((𝜑𝜒) ∧ 𝜓))
Colors of variables: wff set class
Syntax hints:  wa 103  wb 104  w3a 947
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107
This theorem depends on definitions:  df-bi 116  df-3an 949
This theorem is referenced by:  anandi3r  961  dff1o3  5341
  Copyright terms: Public domain W3C validator