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Metamath Proof Explorer

Theorem iniin1

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

		Ref	Expression
	Assertion	iniin1	$⊢ A \neq \emptyset \to ⋂_{x \in A} C \cap B = ⋂_{x \in A} (C \cap B)$

Step	Hyp	Ref	Expression
1		iinin1	$⊢ A \neq \emptyset \to ⋂_{x \in A} (C \cap B) = ⋂_{x \in A} C \cap B$
2	1	eqcomd	$⊢ A \neq \emptyset \to ⋂_{x \in A} C \cap B = ⋂_{x \in A} (C \cap B)$