\begin{frame}{Also Satisfiability is Undecidable}
  \begin{proposition}
    For sentences $\aform$ it holds:
    \begin{talign}
      \text{$\aform$ is unsatisfiable} \;\; & \Longleftrightarrow\;\; \text{$\formula{\lognot{\aform}}$ is valid}  
      \\
      \mpause[1]{ \text{$\aform$ is satisfiable} \;\; & \Longleftrightarrow\;\; \text{$\formula{\lognot{\aform}}$ is not valid} }
    \end{talign}
  \end{proposition}  
  \updatepause\bigskip
  
  Since this defines an easy reduction of the 
  validity problem to the satisfiability problem.
  It follows immediately:  
  \begin{block}{Theorem}
    The \emph{satisfiability problem} in predicate logic is \alert{undecidable}.
  \end{block}
\end{frame}