 The theorem states that for any complete varieties "U", "V" and "W" over an algebraically closed field, and given points "u", "v" and "w" on them, any invertible sheaf "L" which has a trivial restriction to each of "U"× "V" × {"w"}, "U"× {"v"} × "W", and {"u"} × "V" × "W", is itself trivial.