Theorem necon2bbii

Description: Contrapositive inference for inequality. (Contributed by NM, 13-Apr-2007)

	Ref	Expression
Hypothesis	necon2bbii.1	$$⊢\phi \leftrightarrow A\ne B$$
Assertion	necon2bbii	$$⊢A=B\leftrightarrow \neg \phi$$

Proof

Step	Hyp	Ref	Expression
1		necon2bbii.1	$$⊢\phi \leftrightarrow A\ne B$$
2	1	bicomi	$$⊢A\ne B\leftrightarrow \phi$$
3	2	necon1bbii	$$⊢\neg \phi \leftrightarrow A=B$$
4	3	bicomi	$$⊢A=B\leftrightarrow \neg \phi$$