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

Theorem fal 1371
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 1368 . . 3  |- T.
21notnoti 646 . 2  |-  -.  -. T.
3 df-fal 1370 . 2  |-  ( F.  <->  -. T.  )
42, 3mtbir 672 1  |-  -. F.
Colors of variables: wff set class
Syntax hints:   -. wn 3   T. wtru 1365   F. wfal 1369
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-in1 615  ax-in2 616
This theorem depends on definitions:  df-bi 117  df-tru 1367  df-fal 1370
This theorem is referenced by:  nbfal  1375  bifal  1377  falim  1378  dfnot  1382  notfal  1425  alnex  1510  csbprc  3483  bj-stfal  14931  bj-dcfal  14944  bdnth  15023
  Copyright terms: Public domain W3C validator