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Metamath Proof Explorer

Theorem nel2nelini

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

		Ref	Expression
	Hypothesis	nel2nelini.1	$⊢ \neg A \in C$
	Assertion	nel2nelini	$⊢ \neg A \in (B \cap C)$

Step	Hyp	Ref	Expression
1		nel2nelini.1	$⊢ \neg A \in C$
2		nel2nelin	$⊢ \neg A \in C \to \neg A \in (B \cap C)$
3	1 2	ax-mp	$⊢ \neg A \in (B \cap C)$