ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  pm2.81 GIF version

Theorem pm2.81 785
Description: Theorem *2.81 of [WhiteheadRussell] p. 108. (Contributed by NM, 3-Jan-2005.)
Assertion
Ref Expression
pm2.81 ((𝜓 → (𝜒𝜃)) → ((𝜑𝜓) → ((𝜑𝜒) → (𝜑𝜃))))

Proof of Theorem pm2.81
StepHypRef Expression
1 orim2 763 . 2 ((𝜓 → (𝜒𝜃)) → ((𝜑𝜓) → (𝜑 ∨ (𝜒𝜃))))
2 pm2.76 782 . 2 ((𝜑 ∨ (𝜒𝜃)) → ((𝜑𝜒) → (𝜑𝜃)))
31, 2syl6 33 1 ((𝜓 → (𝜒𝜃)) → ((𝜑𝜓) → ((𝜑𝜒) → (𝜑𝜃))))
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