ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  pm5.42 GIF version

Theorem pm5.42 307
Description: Theorem *5.42 of [WhiteheadRussell] p. 125. (Contributed by NM, 3-Jan-2005.)
Assertion
Ref Expression
pm5.42 ((𝜑 → (𝜓𝜒)) ↔ (𝜑 → (𝜓 → (𝜑𝜒))))

Proof of Theorem pm5.42
StepHypRef Expression
1 ibar 289 . . 3 (𝜑 → (𝜒 ↔ (𝜑𝜒)))
21imbi2d 223 . 2 (𝜑 → ((𝜓𝜒) ↔ (𝜓 → (𝜑𝜒))))
32pm5.74i 173 1 ((𝜑 → (𝜓𝜒)) ↔ (𝜑 → (𝜓 → (𝜑𝜒))))
Colors of variables: wff set class
Syntax hints:  wi 4  wa 101  wb 102
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105
This theorem depends on definitions:  df-bi 114
This theorem is referenced by:  anc2l  314  imdistan  426
  Copyright terms: Public domain W3C validator