Theorem fal 1402

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 1399	. . 3 |- T.
2	1	notnoti 648	. 2 |- -. -. T.
3		df-fal 1401	. 2 |- ( F. <-> -. T. )
4	2, 3	mtbir 675	1 |- -. F.

Syntax hints:   -. wn 3   T. wtru 1396   F. wfal 1400

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 617  ax-in2 618

This theorem depends on definitions:  df-bi 117  df-tru 1398  df-fal 1401

This theorem is referenced by:  nbfal  1406  bifal  1408  falim  1409  dfnot  1413  notfal  1456  alnex  1545  csbprc  3537  bj-stfal  16106  bj-dcfal  16119  bdnth  16197