Theorem notfal 1360

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 1306	. 2 ⊢ ¬ ⊥
2	1	bitru 1311	1 ⊢ (¬ ⊥ ↔ ⊤)

Syntax hints:  ¬ wn 3   ↔ wb 104  ⊤wtru 1300  ⊥wfal 1304

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-in1 584  ax-in2 585

This theorem depends on definitions:  df-bi 116  df-tru 1302  df-fal 1305

This theorem is referenced by:  truxorfal  1366  falxortru  1367  falxorfal  1368