Theorem fal 1404

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 1401	. . 3 ⊢ ⊤
2	1	notnoti 650	. 2 ⊢ ¬ ¬ ⊤
3		df-fal 1403	. 2 ⊢ (⊥ ↔ ¬ ⊤)
4	2, 3	mtbir 677	1 ⊢ ¬ ⊥

Syntax hints:  ¬ wn 3  ⊤wtru 1398  ⊥wfal 1402

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 1400  df-fal 1403

This theorem is referenced by:  nbfal  1408  bifal  1410  falim  1411  dfnot  1415  notfal  1458  alnex  1547  csbprc  3540  bj-stfal  16338  bj-dcfal  16351  bdnth  16429