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Metamath Proof Explorer

Theorem elinel1

Description: Membership in an intersection implies membership in the first set. (Contributed by Glauco Siliprandi, 11-Dec-2019)

		Ref	Expression
	Assertion	elinel1	$⊢ A \in (B \cap C) \to A \in B$

Step	Hyp	Ref	Expression
1		elin	$⊢ A \in (B \cap C) \leftrightarrow (A \in B \land A \in C)$
2	1	simplbi	$⊢ A \in (B \cap C) \to A \in B$