documentclass{article}
usepackage{logicproof}

begin{document}

  begin{logicproof}{1}
    P lor Q & premise\
    Z & premise\
    begin{subproof}
      P & [assume]\
        [dots] &\
          &
    end{subproof}
    begin{subproof}
        Q & [assume]\
        [dots] &\
          &
    end{subproof}
    (P lor Q) land Z & el 3--4 5--6
  end{logicproof}

end{document}