Theorem trunantru

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

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

Proof

Step	Hyp	Ref	Expression
1		nannot	⊢ ( ¬ ⊤ ↔ ( ⊤ ⊼ ⊤ ) )
2		nottru	⊢ ( ¬ ⊤ ↔ ⊥ )
3	1 2	bitr3i	⊢ ( ( ⊤ ⊼ ⊤ ) ↔ ⊥ )