Metamath Proof Explorer

Theorem elinel2

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

		Ref	Expression
	Assertion	elinel2	$⊢ A \in (B \cap C) \to A \in C$

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