Theorem falnanfal

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

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

Proof

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