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Theorem fal 1319
Description: The truth value is refutable. (Contributed by Anthony Hart, 22-Oct-2010.) (Proof shortened by Mel L. O'Cat, 11-Mar-2012.)
Assertion
Ref Expression
fal ¬ ⊥

Proof of Theorem fal
StepHypRef Expression
1 tru 1316 . . 3
21notnoti 617 . 2 ¬ ¬ ⊤
3 df-fal 1318 . 2 (⊥ ↔ ¬ ⊤)
42, 3mtbir 643 1 ¬ ⊥
Colors of variables: wff set class
Syntax hints:  ¬ wn 3  wtru 1313  wfal 1317
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-in1 586  ax-in2 587
This theorem depends on definitions:  df-bi 116  df-tru 1315  df-fal 1318
This theorem is referenced by:  nbfal  1323  bifal  1325  falim  1326  dfnot  1330  notfal  1373  alnex  1456  csbprc  3372  bdnth  12715
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