Theorem neeq2

Description: Equality theorem for inequality. (Contributed by NM, 19-Nov-1994) (Proof shortened by Wolf Lammen, 18-Nov-2019)

	Ref	Expression
Assertion	neeq2	$$⊢A=B\to \left(C\ne A\leftrightarrow C\ne B\right)$$

Proof

Step	Hyp	Ref	Expression
1		id	$$⊢A=B\to A=B$$
2	1	neeq2d	$$⊢A=B\to \left(C\ne A\leftrightarrow C\ne B\right)$$