Theorem notfal 1349

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 1322	. 2 ⊢ ¬ ⊥
2	1	bitru 1326	1 ⊢ (¬ ⊥ ↔ ⊤ )

Syntax hints:  ¬ wn 3   ↔ wb 176   ⊤ 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:  trunanfal  1355  falnanfal  1357  truxorfal  1359  falxortru  1360