Theorem necon2abii

Description: Contrapositive inference for inequality. (Contributed by NM, 2-Mar-2007)

	Ref	Expression
Hypothesis	necon2abii.1	$$⊢A=B\leftrightarrow \neg \phi$$
Assertion	necon2abii	$$⊢\phi \leftrightarrow A\ne B$$

Proof

Step	Hyp	Ref	Expression
1		necon2abii.1	$$⊢A=B\leftrightarrow \neg \phi$$
2	1	bicomi	$$⊢\neg \phi \leftrightarrow A=B$$
3	2	necon1abii	$$⊢A\ne B\leftrightarrow \phi$$
4	3	bicomi	$$⊢\phi \leftrightarrow A\ne B$$