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

Theorem biortn 937
Description: A wff is equivalent to its negated disjunction with falsehood. (Contributed by NM, 9-Jul-2012.)
Assertion
Ref Expression
biortn (𝜑 → (𝜓 ↔ (¬ 𝜑𝜓)))

Proof of Theorem biortn
StepHypRef Expression
1 notnot 142 . 2 (𝜑 → ¬ ¬ 𝜑)
2 biorf 936 . 2 (¬ ¬ 𝜑 → (𝜓 ↔ (¬ 𝜑𝜓)))
31, 2syl 17 1 (𝜑 → (𝜓 ↔ (¬ 𝜑𝜓)))
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wi 4  wb 205  wo 846
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 206  df-or 847
This theorem is referenced by:  oranabs  999  xrdifh  31725  ballotlemfc0  33132  ballotlemfcc  33133  topdifinfindis  35846  topdifinffinlem  35847  4atlem3a  38089  4atlem3b  38090  ntrneineine1lem  42430
  Copyright terms: Public domain W3C validator