Theorem necon1ai

Description: Contrapositive inference for inequality. (Contributed by NM, 12-Feb-2007) (Proof shortened by Wolf Lammen, 22-Nov-2019)

	Ref	Expression
Hypothesis	necon1ai.1	$$⊢\neg \phi \to A=B$$
Assertion	necon1ai	$$⊢A\ne B\to \phi$$

Proof

Step	Hyp	Ref	Expression
1		necon1ai.1	$$⊢\neg \phi \to A=B$$
2	1	necon3ai	$$⊢A\ne B\to \neg \neg \phi$$
3	2	notnotrd	$$⊢A\ne B\to \phi$$