Theorem fal 1319

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 1316	. . 3 ⊢ ⊤
2	1	notnoti 617	. 2 ⊢ ¬ ¬ ⊤
3		df-fal 1318	. 2 ⊢ (⊥ ↔ ¬ ⊤)
4	2, 3	mtbir 643	1 ⊢ ¬ ⊥

Syntax hints:  ¬ wn 3  ⊤wtru 1313  ⊥wfal 1317

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-in1 586  ax-in2 587

This theorem depends on definitions:  df-bi 116  df-tru 1315  df-fal 1318

This theorem is referenced by:  nbfal  1323  bifal  1325  falim  1326  dfnot  1330  notfal  1373  alnex  1456  csbprc  3372  bdnth  12715