Theorem trunantru 1610

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 1528	. 2 ⊢ (¬ ⊤ ↔ (⊤ ⊼ ⊤))
2		nottru 1596	. 2 ⊢ (¬ ⊤ ↔ ⊥)
3	1, 2	bitr3i 280	1 ⊢ ((⊤ ⊼ ⊤) ↔ ⊥)

This proof depends on syntax axioms:  ¬ wn 3   ↔ wb 209   ⊼ wnan 1520  ⊤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-an 401  df-nan 1521  df-fal 1582

This theorem is used by: (None)