Theorem fal 1379

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 1376	. . 3 ⊢ ⊤
2	1	notnoti 646	. 2 ⊢ ¬ ¬ ⊤
3		df-fal 1378	. 2 ⊢ (⊥ ↔ ¬ ⊤)
4	2, 3	mtbir 672	1 ⊢ ¬ ⊥

Syntax hints:  ¬ wn 3  ⊤wtru 1373  ⊥wfal 1377

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 615  ax-in2 616

This theorem depends on definitions:  df-bi 117  df-tru 1375  df-fal 1378

This theorem is referenced by:  nbfal  1383  bifal  1385  falim  1386  dfnot  1390  notfal  1433  alnex  1521  csbprc  3505  bj-stfal  15542  bj-dcfal  15555  bdnth  15634