Theorem fal 1402

Description: The truth value ⊥ is refutable. (Contributed by Anthony Hart, 22-Oct-2010.) (Proof shortened by Mel L. O'Cat, 11-Mar-2012.)

Assertion

Ref	Expression
fal	⊢ ¬ ⊥

Proof of Theorem fal

Step	Hyp	Ref	Expression
1		tru 1399	. . 3 ⊢ ⊤
2	1	notnoti 648	. 2 ⊢ ¬ ¬ ⊤
3		df-fal 1401	. 2 ⊢ (⊥ ↔ ¬ ⊤)
4	2, 3	mtbir 675	1 ⊢ ¬ ⊥

Syntax hints:  ¬ wn 3  ⊤wtru 1396  ⊥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  16064  bj-dcfal  16077  bdnth  16155