Theorem trunantru 1354

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 1293	. 2 ⊢ (¬ ⊤ ↔ ( ⊤ ⊼ ⊤ ))
2		nottru 1348	. 2 ⊢ (¬ ⊤ ↔ ⊥ )
3	1, 2	bitr3i 242	1 ⊢ (( ⊤ ⊼ ⊤ ) ↔ ⊥ )

This proof depends on syntax axioms:  ¬ wn 3   ↔ wb 176   ⊼ wnan 1287   ⊤ wtru 1316   ⊥ wfal 1317

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This proof depends on definitions:  df-bi 177  df-an 360  df-nan 1288  df-fal 1320

This theorem is used by: (None)