Theorem truxortru

Description: A \/_ identity. (Contributed by David A. Wheeler, 8-May-2015)

	Ref	Expression
Assertion	truxortru	⊢ ( ( ⊤ ⊻ ⊤ ) ↔ ⊥ )

Proof

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