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Metamath Proof Explorer

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	$⊢ A \notin B$

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	$⊢ A \notin B$