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

Theorem bianabs 611
Description: Absorb a hypothesis into the second member of a biconditional. (Contributed by FL, 15-Feb-2007.)
Hypothesis
Ref Expression
bianabs.1 (𝜑 → (𝜓 ↔ (𝜑𝜒)))
Assertion
Ref Expression
bianabs (𝜑 → (𝜓𝜒))

Proof of Theorem bianabs
StepHypRef Expression
1 bianabs.1 . 2 (𝜑 → (𝜓 ↔ (𝜑𝜒)))
2 ibar 301 . 2 (𝜑 → (𝜒 ↔ (𝜑𝜒)))
31, 2bitr4d 191 1 (𝜑 → (𝜓𝜒))
Colors of variables: wff set class
Syntax hints:  wi 4  wa 104  wb 105
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108
This theorem depends on definitions:  df-bi 117
This theorem is referenced by:  ceqsrexv  2879  opelopab2a  4277  ov  6007  ovg  6026  ltresr  7851
  Copyright terms: Public domain W3C validator