\begin{frame}
  \frametitle{Proof by Contradiction}
  
  Assume that you have derived
  \begin{align*}
    \parbox{.8cm}{\centerline{$\neg\alpha$}\centerline{$\vdots$}\centerline{$\bot$}}    
  \end{align*}
  \pause

  Then also
  \begin{align*}
    \parbox{3cm}{
    \framebox{\parbox{.8cm}{\centerline{$\neg\alpha$}\centerline{$\vdots$}\centerline{$\bot$}}}\\[1ex]
    $\neg\neg \alpha$ \quad\quad $\neg_i$\\[.5ex]
    $\alpha\hphantom{\neg\neg}$ \quad\quad $\neg\neg_e$
    }
  \end{align*}
  \pause
  
  This is known as \emph{Proof by Contradiction (PBC)}! 
  \pause\smallskip
  
  Also known as \emph{Reductio ad Absurdum (RAA)}!
\end{frame}