Theorem trunantru 1580

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 1494	. 2 ⊢ (¬ ⊤ ↔ (⊤ ⊼ ⊤))
2		nottru 1566	. 2 ⊢ (¬ ⊤ ↔ ⊥)
3	1, 2	bitr3i 276	1 ⊢ ((⊤ ⊼ ⊤) ↔ ⊥)

Syntax hints:  ¬ wn 3   ↔ wb 205   ⊼ wnan 1486  ⊤wtru 1540  ⊥wfal 1551

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 397  df-nan 1487  df-fal 1552

This theorem is referenced by: (None)