Theorem nne

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

	Ref	Expression
Assertion	nne	$$⊢\neg A\ne B\leftrightarrow A=B$$

Proof

Step	Hyp	Ref	Expression
1		df-ne	$$⊢A\ne B\leftrightarrow \neg A=B$$
2	1	con2bii	$$⊢A=B\leftrightarrow \neg A\ne B$$
3	2	bicomi	$$⊢\neg A\ne B\leftrightarrow A=B$$