Let R be an integral domain, and let A,A₁,A₂,…,A_s be overrings of R, where A is of the form S⁻¹R, where S=R∖𝖕₁∪⋯∪𝖕_n for some prime ideals 𝖕_i, and where each A_i, i≥2, is of the form for some multiplicatively closed subset S_i of R. It is shown that if A⊆A₁∪⋯∪A_s, then A⊆A_i for some i.