Theorem notfal 1596

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 1582	. 2 ⊢ ¬ ⊥
2	1	bitru 1577	1 ⊢ (¬ ⊥ ↔ ⊤)

Syntax hints:  ¬ wn 3   ↔ wb 209  ⊤wtru 1569  ⊥wfal 1580

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 210  df-tru 1571  df-fal 1581

This theorem is referenced by:  trunanfal  1610  falnanfal  1612  truxorfal  1614  falnorfal  1620  wl-1xor  38072  ifpdfnan  44160