Theorem notfal 1598

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 1584	. 2 ⊢ ¬ ⊥
2	1	bitru 1579	1 ⊢ (¬ ⊥ ↔ ⊤)

This proof depends on syntax axioms:  ¬ wn 3   ↔ wb 209  ⊤wtru 1571  ⊥wfal 1582

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 1573  df-fal 1583

This theorem is used by:  trunanfal  1612  falnanfal  1614  truxorfal  1616  falnorfal  1622  wl-1xor  38223  ifpdfnan  44313