Theorem notfal 1565

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 1551	. 2 ⊢ ¬ ⊥
2	1	bitru 1546	1 ⊢ (¬ ⊥ ↔ ⊤)

Syntax hints:  ¬ wn 3   ↔ wb 206  ⊤wtru 1538  ⊥wfal 1549

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 207  df-tru 1540  df-fal 1550

This theorem is referenced by:  trunanfal  1579  falnanfal  1581  truxorfal  1583  falnorfal  1589  wl-1xor  37448  ifpdfnan  43448