Theorem notfal 1409

Description: A ¬ identity. (Contributed by Anthony Hart, 22-Oct-2010.) (Proof shortened by Andrew Salmon, 13-May-2011.)

Assertion

Ref	Expression
notfal	⊢ (¬ ⊥ ↔ ⊤)

Proof of Theorem notfal

Step	Hyp	Ref	Expression
1		fal 1355	. 2 ⊢ ¬ ⊥
2	1	bitru 1360	1 ⊢ (¬ ⊥ ↔ ⊤)

Syntax hints:  ¬ wn 3   ↔ wb 104  ⊤wtru 1349  ⊥wfal 1353

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 609  ax-in2 610

This theorem depends on definitions:  df-bi 116  df-tru 1351  df-fal 1354

This theorem is referenced by:  truxorfal  1415  falxortru  1416  falxorfal  1417