\begin{center}
\begin{tabular}{|c|c|} \hline
\multicolumn{2}{|c|}{inference rules}            \\ \hline\hline
proper                 & improper                \\ \hline\hline
$\land$-introduction   &                         \\
$\land$-elimination    &                         \\
$\lor$-introduction    & $\lor$-elimination      \\
$\implies$-elimination & $\implies$-introduction \\
$\neg$-elimination     & $\neg$-introduction     \\
$\neg\neg$-elimination &                         \\
$\#$-elimination       &                         \\
$\forall$-elimination  & $\forall$-introduction  \\
$\exists$-introduction & $\exists$-elimination   \\ \hline
\end{tabular}
\end{center}


