Theorem necon4i

Description: Contrapositive inference for inequality. (Contributed by NM, 17-Mar-2007) (Proof shortened by Andrew Salmon, 25-May-2011) (Proof shortened by Wolf Lammen, 24-Nov-2019)

	Ref	Expression
Hypothesis	necon4i.1	$$⊢A\ne B\to C\ne D$$
Assertion	necon4i	$$⊢C=D\to A=B$$

Proof

Step	Hyp	Ref	Expression
1		necon4i.1	$$⊢A\ne B\to C\ne D$$
2	1	neneqd	$$⊢A\ne B\to \neg C=D$$
3	2	necon4ai	$$⊢C=D\to A=B$$