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

Theorem norbi 911
Description: If neither of two propositions is true, then these propositions are equivalent. (Contributed by BJ, 26-Apr-2019.)
Assertion
Ref Expression
norbi (¬ (𝜑𝜓) → (𝜑𝜓))

Proof of Theorem norbi
StepHypRef Expression
1 orc 894 . 2 (𝜑 → (𝜑𝜓))
2 olc 895 . 2 (𝜓 → (𝜑𝜓))
31, 2pm5.21ni 369 1 (¬ (𝜑𝜓) → (𝜑𝜓))
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wi 4  wb 198  wo 874
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 199  df-or 875
This theorem is referenced by:  nbior  912  oibabs  975
  Copyright terms: Public domain W3C validator