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Metamath Proof Explorer

Theorem neli

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

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

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