Theorem neir

Description: Inference associated with df-ne . (Contributed by BJ, 7-Jul-2018)

	Ref	Expression
Hypothesis	neir.1	$$⊢\neg A=B$$
Assertion	neir	$$⊢A\ne B$$

Proof

Step	Hyp	Ref	Expression
1		neir.1	$$⊢\neg A=B$$
2		df-ne	$$⊢A\ne B\leftrightarrow \neg A=B$$
3	1 2	mpbir	$$⊢A\ne B$$