\begin{frame}
  \frametitle{The relation of $\models$ and $\vdash$}
  
  \begin{block}{Theorem}
    The \emph{semantic entailment $\models$} and \emph{syntactic derivability $\vdash$}
    coincide:
    \begin{talign}
      \phi_1,\ldots,\phi_n \;\models \; \psi 
      \quad\iff\quad 
      \phi_1,\ldots,\phi_n \;\vdash \; \psi 
    \end{talign}
  \end{block}
  \bigskip\pause
  
  \begin{goal}{Two directions}
    \begin{itemize}
    \item[$\Rightarrow$] \quad  \aemph{Completeness} \\
            \mpause[1]{\quad In a slogan: everything true is derivable.}
            \medskip
    \item[$\Leftarrow$] \quad \aemph{Soundness (or Correctness)} \\
            \mpause{\quad In a slogan: everything derivable is true.}
    \end{itemize}
  \end{goal}  
\end{frame}