Theorem necon2bi

Description: Contrapositive inference for inequality. (Contributed by NM, 1-Apr-2007)

	Ref	Expression
Hypothesis	necon2bi.1	$$⊢\phi \to A\ne B$$
Assertion	necon2bi	$$⊢A=B\to \neg \phi$$

Proof

Step	Hyp	Ref	Expression
1		necon2bi.1	$$⊢\phi \to A\ne B$$
2	1	neneqd	$$⊢\phi \to \neg A=B$$
3	2	con2i	$$⊢A=B\to \neg \phi$$