Theorem necon3i

Description: Contrapositive inference for inequality. (Contributed by NM, 9-Aug-2006) (Proof shortened by Wolf Lammen, 22-Nov-2019)

	Ref	Expression
Hypothesis	necon3i.1	$$⊢A=B\to C=D$$
Assertion	necon3i	$$⊢C\ne D\to A\ne B$$

Proof

Step	Hyp	Ref	Expression
1		necon3i.1	$$⊢A=B\to C=D$$
2	1	necon3ai	$$⊢C\ne D\to \neg A=B$$
3	2	neqned	$$⊢C\ne D\to A\ne B$$