Theorem fal 1355

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 1352	. . 3 |- T.
2	1	notnoti 640	. 2 |- -. -. T.
3		df-fal 1354	. 2 |- ( F. <-> -. T. )
4	2, 3	mtbir 666	1 |- -. F.

Syntax hints:   -. wn 3   T. wtru 1349   F. wfal 1353

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-in1 609  ax-in2 610

This theorem depends on definitions:  df-bi 116  df-tru 1351  df-fal 1354

This theorem is referenced by:  nbfal  1359  bifal  1361  falim  1362  dfnot  1366  notfal  1409  alnex  1492  csbprc  3460  bj-stfal  13777  bj-dcfal  13790  bdnth  13869