J.P.C.Greenlees ``The coefficient ring of equivariant bordism classifies equivariant formal groups over Noetherian rings.'' 19 pp This paper gives the proof of the theorem of the title. Unfortunately this does not determine the coefficient ring of equivariant bordism since it is not itself Noetherian. However a pullback square for A-equivariant bordism is given for any finite abelian group A, generalizing that of tom Dieck and Kriz for groups of prime order. There are a number of useful facts about the universal ring for equivariant formal groups.