ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  pm5.44 GIF version

Theorem pm5.44 834
Description: Theorem *5.44 of [WhiteheadRussell] p. 125. (Contributed by NM, 3-Jan-2005.)
Assertion
Ref Expression
pm5.44 ((𝜑𝜓) → ((𝜑𝜒) ↔ (𝜑 → (𝜓𝜒))))

Proof of Theorem pm5.44
StepHypRef Expression
1 jcab 535 . 2 ((𝜑 → (𝜓𝜒)) ↔ ((𝜑𝜓) ∧ (𝜑𝜒)))
21baibr 829 1 ((𝜑𝜓) → ((𝜑𝜒) ↔ (𝜑 → (𝜓𝜒))))
Colors of variables: wff set class
Syntax hints:  wi 4  wa 97  wb 98
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101
This theorem depends on definitions:  df-bi 110
This theorem is referenced by:  reldisj  3271
  Copyright terms: Public domain W3C validator