Theorem necon1i

Description: Contrapositive inference for inequality. (Contributed by NM, 18-Mar-2007)

	Ref	Expression
Hypothesis	necon1i.1	$$⊢A\ne B\to C=D$$
Assertion	necon1i	$$⊢C\ne D\to A=B$$

Proof

Step	Hyp	Ref	Expression
1		necon1i.1	$$⊢A\ne B\to C=D$$
2		df-ne	$$⊢A\ne B\leftrightarrow \neg A=B$$
3	2 1	sylbir	$$⊢\neg A=B\to C=D$$
4	3	necon1ai	$$⊢C\ne D\to A=B$$