Theorem falxorfal

Description: A \/_ identity. (Contributed by David A. Wheeler, 9-May-2015)

	Ref	Expression
Assertion	falxorfal	⊢ ( ( ⊥ ⊻ ⊥ ) ↔ ⊥ )

Proof

Step	Hyp	Ref	Expression
1		df-xor	⊢ ( ( ⊥ ⊻ ⊥ ) ↔ ¬ ( ⊥ ↔ ⊥ ) )
2		falbifal	⊢ ( ( ⊥ ↔ ⊥ ) ↔ ⊤ )
3	1 2	xchbinx	⊢ ( ( ⊥ ⊻ ⊥ ) ↔ ¬ ⊤ )
4		nottru	⊢ ( ¬ ⊤ ↔ ⊥ )
5	3 4	bitri	⊢ ( ( ⊥ ⊻ ⊥ ) ↔ ⊥ )