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Theorem fal 1235
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 1232 . . 3
21notnoti 561 . 2 ¬ ¬ ⊤
3 df-fal 1234 . 2 ( ⊥ ↔ ¬ ⊤ )
42, 3mtbir 583 1 ¬ ⊥
Colors of variables: wff set class
Syntax hints:  ¬ wn 3  wtru 1229  wfal 1233
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-in1 532  ax-in2 533
This theorem depends on definitions:  df-bi 110  df-tru 1231  df-fal 1234
This theorem is referenced by:  nbfal  1239  bifal  1241  falim  1242  dfnot  1247  notfal  1288  alnex  1369  csbprc  3239  bdnth  7061
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