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

Step	Hyp	Ref	Expression
1		tru 1293	. . 3 |- T.
2	1	notnoti 609	. 2 |- -. -. T.
3		df-fal 1295	. 2 |- ( F. <-> -. T. )
4	2, 3	mtbir 631	1 |- -. F.

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