Theorem notfal 1345

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 1291	. 2 ⊢ ¬ ⊥
2	1	bitru 1296	1 ⊢ (¬ ⊥ ↔ ⊤)

Syntax hints:  ¬ wn 3   ↔ wb 103  ⊤wtru 1285  ⊥wfal 1289

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-in1 576  ax-in2 577

This theorem depends on definitions:  df-bi 115  df-tru 1287  df-fal 1290

This theorem is referenced by:  truxorfal  1351  falxortru  1352  falxorfal  1353