Theorem notfal 1561

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 1547	. 2 ⊢ ¬ ⊥
2	1	bitru 1542	1 ⊢ (¬ ⊥ ↔ ⊤)

Syntax hints:  ¬ wn 3   ↔ wb 205  ⊤wtru 1534  ⊥wfal 1545

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 206  df-tru 1536  df-fal 1546

This theorem is referenced by:  trunanfal  1575  falnanfal  1577  truxorfal  1579  falnorfal  1585  wl-1xor  36864  ifpdfnan  42787