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

Theorem rbaibr 908
Description: Move conjunction outside of biconditional. (Contributed by Mario Carneiro, 11-Sep-2015.)
Hypothesis
Ref Expression
baib.1 (𝜑 ↔ (𝜓𝜒))
Assertion
Ref Expression
rbaibr (𝜒 → (𝜓𝜑))

Proof of Theorem rbaibr
StepHypRef Expression
1 baib.1 . . 3 (𝜑 ↔ (𝜓𝜒))
2 ancom 264 . . 3 ((𝜓𝜒) ↔ (𝜒𝜓))
31, 2bitri 183 . 2 (𝜑 ↔ (𝜒𝜓))
43baibr 906 1 (𝜒 → (𝜓𝜑))
Colors of variables: wff set class
Syntax hints:  wi 4  wa 103  wb 104
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
This theorem is referenced by: (None)
  Copyright terms: Public domain W3C validator