Theorem falnantru

Description: A -/\ identity. (Contributed by Anthony Hart, 23-Oct-2010) (Proof shortened by Andrew Salmon, 13-May-2011)

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

Proof

Step	Hyp	Ref	Expression
1		nancom	⊢ ( ( ⊥ ⊼ ⊤ ) ↔ ( ⊤ ⊼ ⊥ ) )
2		trunanfal	⊢ ( ( ⊤ ⊼ ⊥ ) ↔ ⊤ )
3	1 2	bitri	⊢ ( ( ⊥ ⊼ ⊤ ) ↔ ⊤ )