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

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

\begin{document}

$$
\infer[absurd]{¬(P∧Q),P,Q ⊢ ¬P∨¬Q}{
  \infer[∧~intro]{\cdots ⊢ P∧Q}{
    \infer[assum]{\cdots,P ⊢ P}{}
    &
    \infer[assum]{\cdots,Q ⊢ Q}{}
  }
  &
  \infer[assum]{\cdots, ¬(P∧Q) ⊢ ¬(P∧Q)}{}
}
$$
\end{document}
