Theorem fal 1342

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 1339	. . 3 ⊢ ⊤
2	1	notnoti 635	. 2 ⊢ ¬ ¬ ⊤
3		df-fal 1341	. 2 ⊢ (⊥ ↔ ¬ ⊤)
4	2, 3	mtbir 661	1 ⊢ ¬ ⊥

Syntax hints:  ¬ wn 3  ⊤wtru 1336  ⊥wfal 1340

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-in1 604  ax-in2 605

This theorem depends on definitions:  df-bi 116  df-tru 1338  df-fal 1341

This theorem is referenced by:  nbfal  1346  bifal  1348  falim  1349  dfnot  1353  notfal  1396  alnex  1479  csbprc  3439  bj-stfal  13288  bj-dcfal  13298  bdnth  13380