Theorem nelir

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

	Ref	Expression
Hypothesis	nelir.1	$$⊢\neg A\in B$$
Assertion	nelir	$$⊢A\notin B$$

Proof

Step	Hyp	Ref	Expression
1		nelir.1	$$⊢\neg A\in B$$
2		df-nel	$$⊢A\notin B\leftrightarrow \neg A\in B$$
3	1 2	mpbir	$$⊢A\notin B$$