Theorem fal 1405

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 1402	. . 3 ⊢ ⊤
2	1	notnoti 650	. 2 ⊢ ¬ ¬ ⊤
3		df-fal 1404	. 2 ⊢ (⊥ ↔ ¬ ⊤)
4	2, 3	mtbir 678	1 ⊢ ¬ ⊥

Syntax hints:  ¬ wn 3  ⊤wtru 1399  ⊥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  16443  bj-dcfal  16456  bdnth  16533