Theorem trunantru 1574

Description: A ⊼ identity. (Contributed by Anthony Hart, 22-Oct-2010.) (Proof shortened by Andrew Salmon, 13-May-2011.)

Assertion

Ref	Expression
trunantru	⊢ ((⊤ ⊼ ⊤) ↔ ⊥)

Proof of Theorem trunantru

Step	Hyp	Ref	Expression
1		nannot 1492	. 2 ⊢ (¬ ⊤ ↔ (⊤ ⊼ ⊤))
2		nottru 1560	. 2 ⊢ (¬ ⊤ ↔ ⊥)
3	1, 2	bitr3i 277	1 ⊢ ((⊤ ⊼ ⊤) ↔ ⊥)

Syntax hints:  ¬ wn 3   ↔ wb 205   ⊼ wnan 1484  ⊤wtru 1534  ⊥wfal 1545

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 206  df-an 396  df-nan 1485  df-fal 1546

This theorem is referenced by: (None)