Theorem nottru 1596

Description: A ¬ identity. (Contributed by Anthony Hart, 22-Oct-2010.)

Assertion

Ref	Expression
nottru	⊢ (¬ ⊤ ↔ ⊥)

Proof of Theorem nottru

Step	Hyp	Ref	Expression
1		df-fal 1582	. 2 ⊢ (⊥ ↔ ¬ ⊤)
2	1	bicomi 227	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-fal 1582

This theorem is used by:  trunantru  1610  truxortru  1614  falxorfal  1617