We prove that if G(R)=Gπ(Φ,R)\documentclass[12pt]{minimal}
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\begin{document}$$G(R)=G_\pi (\Phi ,R)$$\end{document}(E(R)=Eπ(Φ,R))\documentclass[12pt]{minimal}
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\begin{document}$$(E(R)=E_{\pi }(\Phi , R))$$\end{document} is an (elementary) Chevalley group of rank >1\documentclass[12pt]{minimal}
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\begin{document}$$> 1$$\end{document}, R is a local ring (with 12\documentclass[12pt]{minimal}
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\begin{document}$$\frac{1}{2}$$\end{document} for the root systems A2,Bl,Cl,F4,G2\documentclass[12pt]{minimal}
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\begin{document}$${{\textbf{A}}}_2, {{\textbf{B}}}_l, {{\textbf{C}}}_l, {{\textbf{F}}}_4, {{\textbf{G}}}_2$$\end{document} and with 13\documentclass[12pt]{minimal}
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\begin{document}$$\frac{1}{3}$$\end{document} for G2)\documentclass[12pt]{minimal}
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\begin{document}$${{\textbf{G}}}_{2})$$\end{document}, then the group G(R) (or (E(R)) is regularly bi-interpretable with the ring R. As a consequence of this theorem, we show that the class of all Chevalley groups over local rings (with the listed restrictions) is elementarily definable, i.e., if for an arbitrary group H we have H≡Gπ(Φ,R)\documentclass[12pt]{minimal}
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\begin{document}$$H\equiv G_\pi (\Phi , R)$$\end{document}, then there exists a ring R′≡R\documentclass[12pt]{minimal}
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\begin{document}$$R'\equiv R$$\end{document} such that H≅Gπ(Φ,R′)\documentclass[12pt]{minimal}
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\begin{document}$$H\cong G_\pi (\Phi ,R')$$\end{document}.
