Theorem fal 1250

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

Step	Hyp	Ref	Expression
1		tru 1247	. . 3 |- T.
2	1	notnoti 574	. 2 |- -. -. T.
3		df-fal 1249	. 2 |- ( F. <-> -. T. )
4	2, 3	mtbir 596	1 |- -. F.

Syntax hints:   -. wn 3   T. wtru 1244   F. wfal 1248

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 544  ax-in2 545

This theorem depends on definitions:  df-bi 110  df-tru 1246  df-fal 1249

This theorem is referenced by:  nbfal  1254  bifal  1256  falim  1257  dfnot  1262  notfal  1305  alnex  1388  csbprc  3262  bdnth  9954