Theorem nne

Description: Negation of inequality. (Contributed by NM, 9-Jun-2006)

	Ref	Expression
Assertion	nne	⊢ ( ¬ 𝐴 ≠ 𝐵 ↔ 𝐴 = 𝐵 )

Proof

Step	Hyp	Ref	Expression
1		df-ne	⊢ ( 𝐴 ≠ 𝐵 ↔ ¬ 𝐴 = 𝐵 )
2	1	con2bii	⊢ ( 𝐴 = 𝐵 ↔ ¬ 𝐴 ≠ 𝐵 )
3	2	bicomi	⊢ ( ¬ 𝐴 ≠ 𝐵 ↔ 𝐴 = 𝐵 )