\documentclass[convert={outfile=\jobname.svg}]{standalone}

\usepackage{proof}
\usepackage{amsmath}
\usepackage{utf8}

\begin{document}

$$
\infer[\textit{(name)}]{\textit{assumptions} ⊢ \textit{conclusion}}{
  \textit{assumptions for premise 1} ⊢ \textit{premise 1} \qquad &
  \textit{assumptions for premise 2} ⊢ \textit{premise 2} \qquad &
  \cdots
}
$$

\end{document}
