Theorem falnorfal

Description: A -\/ identity. (Contributed by Remi, 25-Oct-2023) (Proof shortened by Wolf Lammen, 17-Dec-2023)

	Ref	Expression
Assertion	falnorfal	⊢ ( ( ⊥ ⊽ ⊥ ) ↔ ⊤ )

Proof

Step	Hyp	Ref	Expression
1		df-nor	⊢ ( ( ⊥ ⊽ ⊥ ) ↔ ¬ ( ⊥ ∨ ⊥ ) )
2		falorfal	⊢ ( ( ⊥ ∨ ⊥ ) ↔ ⊥ )
3	1 2	xchbinx	⊢ ( ( ⊥ ⊽ ⊥ ) ↔ ¬ ⊥ )
4		notfal	⊢ ( ¬ ⊥ ↔ ⊤ )
5	3 4	bitri	⊢ ( ( ⊥ ⊽ ⊥ ) ↔ ⊤ )