I agree with Jubobs comment: using "Theorem 1.2" is very likely to be confusing.
Here's how one might do:
\documentclass{article}
\usepackage{enumitem}
\newenvironment{thmenum}
{\begin{enumerate}[label=\upshape(\arabic),ref=\thethm(\arabic)]}
{\end{enumerate}}
\newtheorem{thm}{Theorem}
\begin{document}
\begin{thm}
The following are true:
\begin{thmenum}
\item \label{foo} Foo
\item \label{bar} Bar
\item \label{baz} Baz
\end{thmenum}
\end{thm}
Refer to Theorem \ref{bar}
\end{document}
I'd give the items a distinctive numbering, so that it will be clearer that "Theorem 1(2)" refers to statement 2 in theorem 1.

Edit for feature request
\documentclass{article}
\usepackage{amsthm}
\usepackage{enumitem}
\NewDocumentCommand{\refprefix}{m}{%
\ifinproofref\else #1\fi
}
\newif\ifinproofref
\newcommand{\proofref}[1]{\begingroup\inproofreftrue\ref{#1}\endgroup}
\newenvironment{thmenum}
{\begin{enumerate}[label=\upshape(\arabic),ref=\refprefix{\thethm}(\arabic)]}
{\end{enumerate}}
\newtheorem{thm}{Theorem}
\begin{document}
\begin{thm}
The following are true:
\begin{thmenum}
\item \label{foo} Foo
\item \label{bar} Bar
\item \label{baz} Baz
\end{thmenum}
\end{thm}
\begin{proof}
\proofref{foo} is easy. \proofref{bar} is not difficult and
immediately proves also~\proofref{baz}.
\end{proof}
Refer to Theorem~\ref{bar}
\end{document}
The format of the ref is made so \thethm can be omitted. You have to use \proofref when referring to the item.
