\begin{frame} \frametitle{Rules for $\neg$ and $\bot$} \begin{goal}{Rules for $\neg$ and $\bot$} \vspace{-1ex} \begin{align*} \infer[\rulename{\neg_e}] {\bot} {\alpha && \neg \alpha} \end{align*} \pause \begin{align*} \infer[\rulename{\neg_i}] {\neg \alpha} { \framebox{\parbox{.8cm}{\centerline{$\alpha$}\centerline{$\vdots$}\centerline{$\bot$}}} } \end{align*} \pause \begin{align*} \infer[\rulename{\bot_e}] {\alpha} {\bot} \end{align*} \end{goal} \end{frame}