Theorem necon1bbii

Description: Contrapositive inference for inequality. (Contributed by NM, 17-Mar-2007) (Proof shortened by Wolf Lammen, 24-Nov-2019)

	Ref	Expression
Hypothesis	necon1bbii.1	$$⊢A\ne B\leftrightarrow \phi$$
Assertion	necon1bbii	$$⊢\neg \phi \leftrightarrow A=B$$

Proof

Step	Hyp	Ref	Expression
1		necon1bbii.1	$$⊢A\ne B\leftrightarrow \phi$$
2		nne	$$⊢\neg A\ne B\leftrightarrow A=B$$
3	2 1	xchnxbi	$$⊢\neg \phi \leftrightarrow A=B$$