Theorem fal 1360

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 1357	. . 3 ⊢ ⊤
2	1	notnoti 645	. 2 ⊢ ¬ ¬ ⊤
3		df-fal 1359	. 2 ⊢ (⊥ ↔ ¬ ⊤)
4	2, 3	mtbir 671	1 ⊢ ¬ ⊥

Syntax hints:  ¬ wn 3  ⊤wtru 1354  ⊥wfal 1358

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-in1 614  ax-in2 615

This theorem depends on definitions:  df-bi 117  df-tru 1356  df-fal 1359

This theorem is referenced by:  nbfal  1364  bifal  1366  falim  1367  dfnot  1371  notfal  1414  alnex  1499  csbprc  3469  bj-stfal  14497  bj-dcfal  14510  bdnth  14589