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Metamath Proof Explorer

Theorem nel1nelin

Description: Membership in an intersection implies membership in the first set. (Contributed by Glauco Siliprandi, 2-Jan-2022)

		Ref	Expression
	Assertion	nel1nelin	$⊢ \neg A \in B \to \neg A \in (B \cap C)$

Step	Hyp	Ref	Expression
1		elinel1	$⊢ A \in (B \cap C) \to A \in B$
2	1	con3i	$⊢ \neg A \in B \to \neg A \in (B \cap C)$