Theorem trubifal

Description: A <-> identity. (Contributed by Anthony Hart, 22-Oct-2010) (Proof shortened by Andrew Salmon, 13-May-2011) (Proof shortened by Wolf Lammen, 10-Jul-2020)

	Ref	Expression
Assertion	trubifal	⊢ ( ( ⊤ ↔ ⊥ ) ↔ ⊥ )

Proof

Step	Hyp	Ref	Expression
1		bicom	⊢ ( ( ⊤ ↔ ⊥ ) ↔ ( ⊥ ↔ ⊤ ) )
2		falbitru	⊢ ( ( ⊥ ↔ ⊤ ) ↔ ⊥ )
3	1 2	bitri	⊢ ( ( ⊤ ↔ ⊥ ) ↔ ⊥ )