Theorem fal 1250

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 1247	. . 3 ⊢ ⊤
2	1	notnoti 574	. 2 ⊢ ¬ ¬ ⊤
3		df-fal 1249	. 2 ⊢ (⊥ ↔ ¬ ⊤)
4	2, 3	mtbir 596	1 ⊢ ¬ ⊥

Syntax hints:  ¬ wn 3  ⊤wtru 1244  ⊥wfal 1248

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-in1 544  ax-in2 545

This theorem depends on definitions:  df-bi 110  df-tru 1246  df-fal 1249

This theorem is referenced by:  nbfal  1254  bifal  1256  falim  1257  dfnot  1262  notfal  1305  alnex  1388  csbprc  3262  bdnth  9954