ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  con2biidc GIF version

Theorem con2biidc 879
Description: A contraposition inference. (Contributed by Jim Kingdon, 15-Mar-2018.)
Hypothesis
Ref Expression
con2biidc.1 (DECID 𝜓 → (𝜑 ↔ ¬ 𝜓))
Assertion
Ref Expression
con2biidc (DECID 𝜓 → (𝜓 ↔ ¬ 𝜑))

Proof of Theorem con2biidc
StepHypRef Expression
1 con2biidc.1 . . . 4 (DECID 𝜓 → (𝜑 ↔ ¬ 𝜓))
21bicomd 141 . . 3 (DECID 𝜓 → (¬ 𝜓𝜑))
32con1biidc 877 . 2 (DECID 𝜓 → (¬ 𝜑𝜓))
43bicomd 141 1 (DECID 𝜓 → (𝜓 ↔ ¬ 𝜑))
Colors of variables: wff set class
Syntax hints:  ¬ wn 3  wi 4  wb 105  DECID wdc 834
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-in1 614  ax-in2 615  ax-io 709
This theorem depends on definitions:  df-bi 117  df-dc 835
This theorem is referenced by:  dfexdc  1501  nnedc  2352
  Copyright terms: Public domain W3C validator