Users' Mathboxes Mathbox for ML < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  con1bii2 Structured version   Visualization version   GIF version

Theorem con1bii2 34750
Description: A contraposition inference. (Contributed by ML, 18-Oct-2020.)
Hypothesis
Ref Expression
con1bii2.1 𝜑𝜓)
Assertion
Ref Expression
con1bii2 (𝜑 ↔ ¬ 𝜓)

Proof of Theorem con1bii2
StepHypRef Expression
1 con1bii2.1 . . 3 𝜑𝜓)
21con1bii 360 . 2 𝜓𝜑)
32bicomi 227 1 (𝜑 ↔ ¬ 𝜓)
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wb 209
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8
This theorem depends on definitions:  df-bi 210
This theorem is referenced by: (None)
  Copyright terms: Public domain W3C validator