Theorem fal 1291

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 1288	. . 3 ⊢ ⊤
2	1	notnoti 606	. 2 ⊢ ¬ ¬ ⊤
3		df-fal 1290	. 2 ⊢ (⊥ ↔ ¬ ⊤)
4	2, 3	mtbir 628	1 ⊢ ¬ ⊥

Syntax hints:  ¬ wn 3  ⊤wtru 1285  ⊥wfal 1289

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-in1 576  ax-in2 577

This theorem depends on definitions:  df-bi 115  df-tru 1287  df-fal 1290

This theorem is referenced by:  nbfal  1295  bifal  1297  falim  1298  dfnot  1302  notfal  1345  alnex  1428  csbprc  3289  bdnth  10625