Theorem fal 1322

Description: ⊥ 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 1321	. . 3 ⊢ ⊤
2	1	notnoti 115	. 2 ⊢ ¬ ¬ ⊤
3		df-fal 1320	. 2 ⊢ ( ⊥ ↔ ¬ ⊤ )
4	2, 3	mtbir 290	1 ⊢ ¬ ⊥

Syntax hints:  ¬ wn 3   ⊤ wtru 1316   ⊥ wfal 1317

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem depends on definitions:  df-bi 177  df-tru 1319  df-fal 1320

This theorem is referenced by:  nbfal  1325  bifal  1327  falim  1328  truanfal  1337  falantru  1338  notfal  1349