ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  pm2.31 GIF version

Theorem pm2.31 742
Description: Theorem *2.31 of [WhiteheadRussell] p. 104. (Contributed by NM, 3-Jan-2005.)
Assertion
Ref Expression
pm2.31 ((𝜑 ∨ (𝜓𝜒)) → ((𝜑𝜓) ∨ 𝜒))

Proof of Theorem pm2.31
StepHypRef Expression
1 orass 741 . 2 (((𝜑𝜓) ∨ 𝜒) ↔ (𝜑 ∨ (𝜓𝜒)))
21biimpri 132 1 ((𝜑 ∨ (𝜓𝜒)) → ((𝜑𝜓) ∨ 𝜒))
Colors of variables: wff set class
Syntax hints:  wi 4  wo 682
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 683
This theorem depends on definitions:  df-bi 116
This theorem is referenced by: (None)
  Copyright terms: Public domain W3C validator