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Metamath Proof Explorer

Theorem iniin2

Description: Indexed intersection of intersection. (Contributed by Glauco Siliprandi, 23-Oct-2021)

		Ref	Expression
	Assertion	iniin2	$⊢ A \neq \emptyset \to B \cap ⋂_{x \in A} C = ⋂_{x \in A} (B \cap C)$

Step	Hyp	Ref	Expression
1		iinin2	$⊢ A \neq \emptyset \to ⋂_{x \in A} (B \cap C) = B \cap ⋂_{x \in A} C$
2	1	eqcomd	$⊢ A \neq \emptyset \to B \cap ⋂_{x \in A} C = ⋂_{x \in A} (B \cap C)$