Theorem fal 1409

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 1406	. . 3 ⊢ ⊤
2	1	notnoti 654	. 2 ⊢ ¬ ¬ ⊤
3		df-fal 1408	. 2 ⊢ (⊥ ↔ ¬ ⊤)
4	2, 3	mtbir 682	1 ⊢ ¬ ⊥

This proof depends on syntax axioms:  ¬ wn 3  ⊤wtru 1403  ⊥wfal 1407

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-in1 623  ax-in2 624

This proof depends on definitions:  df-bi 117  df-tru 1405  df-fal 1408

This theorem is used by:  nbfal  1413  bifal  1415  falim  1416  dfnot  1420  notfal  1463  alnex  1552  dfnul3  3524  csbprc  3572  bj-stfal  16770  bj-dcfal  16783  bdnth  16860