Theorem neeq1

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

	Ref	Expression
Assertion	neeq1	$$⊢A=B\to \left(A\ne C\leftrightarrow B\ne C\right)$$

Proof

Step	Hyp	Ref	Expression
1		id	$$⊢A=B\to A=B$$
2	1	neeq1d	$$⊢A=B\to \left(A\ne C\leftrightarrow B\ne C\right)$$