\begin{equation}
  \begin{split}
    (m_1,\, m_2) &\rightarrow \left\{ 
      \begin{array}{p{2cm}l}
        (m_2,\, m_1) & \textrm{I}\\
        m_1 + m_2  & \textrm{II}
      \end{array} \right. \\
   \end{split}
\end{equation}