Theorem neeq2i

Description: Inference for inequality. (Contributed by NM, 29-Apr-2005) (Proof shortened by Wolf Lammen, 19-Nov-2019)

	Ref	Expression
Hypothesis	neeq1i.1	$$⊢A=B$$
Assertion	neeq2i	$$⊢C\ne A\leftrightarrow C\ne B$$

Proof

Step	Hyp	Ref	Expression
1		neeq1i.1	$$⊢A=B$$
2	1	eqeq2i	$$⊢C=A\leftrightarrow C=B$$
3	2	necon3bii	$$⊢C\ne A\leftrightarrow C\ne B$$