ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  fal Unicode version

Theorem fal 1296
Description: The truth value F. is refutable. (Contributed by Anthony Hart, 22-Oct-2010.) (Proof shortened by Mel L. O'Cat, 11-Mar-2012.)
Assertion
Ref Expression
fal  |-  -. F.

Proof of Theorem fal
StepHypRef Expression
1 tru 1293 . . 3  |- T.
21notnoti 609 . 2  |-  -.  -. T.
3 df-fal 1295 . 2  |-  ( F.  <->  -. T.  )
42, 3mtbir 631 1  |-  -. F.
Colors of variables: wff set class
Syntax hints:   -. wn 3   T. wtru 1290   F. wfal 1294
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-in1 579  ax-in2 580
This theorem depends on definitions:  df-bi 115  df-tru 1292  df-fal 1295
This theorem is referenced by:  nbfal  1300  bifal  1302  falim  1303  dfnot  1307  notfal  1350  alnex  1433  csbprc  3325  bdnth  11382
  Copyright terms: Public domain W3C validator