Theorem necon3bbii

Description: Deduction from equality to inequality. (Contributed by NM, 13-Apr-2007)

	Ref	Expression
Hypothesis	necon3bbii.1	$$⊢\phi \leftrightarrow A=B$$
Assertion	necon3bbii	$$⊢\neg \phi \leftrightarrow A\ne B$$

Proof

Step	Hyp	Ref	Expression
1		necon3bbii.1	$$⊢\phi \leftrightarrow A=B$$
2	1	bicomi	$$⊢A=B\leftrightarrow \phi$$
3	2	necon3abii	$$⊢A\ne B\leftrightarrow \neg \phi$$
4	3	bicomi	$$⊢\neg \phi \leftrightarrow A\ne B$$