3/179
\begin{frame}
  \frametitle{Natural Deduction}
  
  \begin{goal}{}
    \vspace{-1.5ex}
    \begin{align*}
      \phi_1,\ldots,\phi_n \;\vdash \; \psi
    \end{align*}
    means: 
    there exists a \emph{natural deduction derivation}
    with 
    \begin{itemize}
      \item premises $\phi_1,\ldots,\phi_n$, and
      \item conclusion $\psi$.
    \end{itemize} 
  \end{goal}
  \pause\bigskip
  
  \begin{alertgoal}{}
    Natural deduction is a \emph{formal system} with \emph{strict formal rules}!
  \end{alertgoal}
\end{frame}