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Metamath Proof Explorer

Theorem nel2nelin

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

		Ref	Expression
	Assertion	nel2nelin	$⊢ \neg A \in C \to \neg A \in (B \cap C)$

Step	Hyp	Ref	Expression
1		elinel2	$⊢ A \in (B \cap C) \to A \in C$
2	1	con3i	$⊢ \neg A \in C \to \neg A \in (B \cap C)$