Theorem fal 1405

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 1402	. . 3 |- T.
2	1	notnoti 650	. 2 |- -. -. T.
3		df-fal 1404	. 2 |- ( F. <-> -. T. )
4	2, 3	mtbir 678	1 |- -. F.

Syntax hints:   -. wn 3   T. wtru 1399   F. wfal 1403

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 619  ax-in2 620

This theorem depends on definitions:  df-bi 117  df-tru 1401  df-fal 1404

This theorem is referenced by:  nbfal  1409  bifal  1411  falim  1412  dfnot  1416  notfal  1459  alnex  1548  csbprc  3542  bj-stfal  16460  bj-dcfal  16473  bdnth  16550