Theorem iniin1

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

	Ref	Expression
Assertion	iniin1	|- ( A =/= (/) -> ( |^|_ x e. A C i^i B ) = |^|_ x e. A ( C i^i B ) )

Proof

Step	Hyp	Ref	Expression
1		iinin1	|- ( A =/= (/) -> |^|_ x e. A ( C i^i B ) = ( |^|_ x e. A C i^i B ) )
2	1	eqcomd	|- ( A =/= (/) -> ( |^|_ x e. A C i^i B ) = |^|_ x e. A ( C i^i B ) )