MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  con1b Structured version   Visualization version   GIF version

Theorem con1b 360
Description: Contraposition. Bidirectional version of con1 148. (Contributed by NM, 3-Jan-1993.)
Assertion
Ref Expression
con1b ((¬ 𝜑𝜓) ↔ (¬ 𝜓𝜑))

Proof of Theorem con1b
StepHypRef Expression
1 con1 148 . 2 ((¬ 𝜑𝜓) → (¬ 𝜓𝜑))
2 con1 148 . 2 ((¬ 𝜓𝜑) → (¬ 𝜑𝜓))
31, 2impbii 210 1 ((¬ 𝜑𝜓) ↔ (¬ 𝜓𝜑))
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wi 4  wb 207
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 208
This theorem is referenced by:  eximal  1774  r19.23v  3276  pwssun  5448  ist1-2  21883  cmpfi  21944  dchrelbas2  25740
  Copyright terms: Public domain W3C validator