\usepackage{fitch}
\usepackage{amsmath}

\begin{document}
$\Large\begin{nd}
  \hypo {h} {\lnot P\lor P}
  \open
    \hypo {np} {\lnot P}
    \open
      \hypo {np-p} {P}
      \have {np-b} {\bot}                      \ne{np,{np-p}}
      \have {np-q} {Q}                         \be{{np-b}}
    \close
    \have {pq} {P\implies Q}                    \ii{{np-p}-{np-q}}
    \have {d1} {(P\implies Q)\lor(Q\implies P)} \oi{pq}
  \close
  \open
    \hypo {p} {P}
    \open
      \hypo {p-q} {Q}
      \have {p-p} {P}                           \r{p}
    \close
    \have {qp} {Q\implies P}                    \ii{{p-q}-{p-p}}
    \have {d2} {(P\implies Q)\lor(Q\implies P)} \oi{qp}
  \close
  \have {d} {(P\implies Q)\lor(Q\implies P)}    \oe{h,np-d1,p-d2}
\end{nd}$
\end{document}