Theorem notfal 1597

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 1583	. 2 ⊢ ¬ ⊥
2	1	bitru 1578	1 ⊢ (¬ ⊥ ↔ ⊤)

This proof depends on syntax axioms:  ¬ wn 3   ↔ wb 209  ⊤wtru 1570  ⊥wfal 1581

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This proof depends on definitions:  df-bi 210  df-tru 1572  df-fal 1582

This theorem is used by:  trunanfal  1611  falnanfal  1613  truxorfal  1615  falnorfal  1621  wl-1xor  38156  ifpdfnan  44240