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

Theorem sylnbir 669
Description: A mixed syllogism inference from a biconditional and an implication. (Contributed by Wolf Lammen, 16-Dec-2013.)
Hypotheses
Ref Expression
sylnbir.1 (𝜓𝜑)
sylnbir.2 𝜓𝜒)
Assertion
Ref Expression
sylnbir 𝜑𝜒)

Proof of Theorem sylnbir
StepHypRef Expression
1 sylnbir.1 . . 3 (𝜓𝜑)
21bicomi 131 . 2 (𝜑𝜓)
3 sylnbir.2 . 2 𝜓𝜒)
42, 3sylnbi 668 1 𝜑𝜒)
Colors of variables: wff set class
Syntax hints:  ¬ wn 3  wi 4  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  ax-in1 604  ax-in2 605
This theorem depends on definitions:  df-bi 116
This theorem is referenced by: (None)
  Copyright terms: Public domain W3C validator