Theorem fal 1380

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 1377	. . 3 |- T.
2	1	notnoti 646	. 2 |- -. -. T.
3		df-fal 1379	. 2 |- ( F. <-> -. T. )
4	2, 3	mtbir 673	1 |- -. F.

Syntax hints:   -. wn 3   T. wtru 1374   F. wfal 1378

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 1376  df-fal 1379

This theorem is referenced by:  nbfal  1384  bifal  1386  falim  1387  dfnot  1391  notfal  1434  alnex  1522  csbprc  3506  bj-stfal  15682  bj-dcfal  15695  bdnth  15774