\begin{frame}
  \frametitle{Semantic Implication / Entailment}
  
  \begin{goal}{We define  \;\;$ \phi_1, \ldots, \phi_n  \; \models \; \psi $\;\;  as} 
  In \aemph{every world} $w$ in \aemph{every Kripke model} $\mathcal{M}$ where 
  \begin{center}
    $\mathcal{M},w \models \phi_1$ and $\ldots$ and $\mathcal{M},w \models \phi_n$
  \end{center}
  it holds also
  \begin{talign}
    \mathcal{M},w \models \psi
  \end{talign}
  \end{goal}
  \smallskip
  \pause

  \begin{exampleblock}{}
    \begin{malign}
      \mpause[1]{\all p \;\mpause{&\not\models}\; \some p } \\
      \mpause{\all p,\; \some q \;\mpause{&\models}\; \some p } \\ 
      \mpause{\all\some p \;\mpause{&\not\models}\; \some\all p } \\
      \mpause{\some\all p \;\mpause{&\not\models}\; \all\some p } \\
      \mpause{\all (p \to q),\; \some p \;\mpause{&\models}\; \some q } 
    \end{malign}
  \end{exampleblock}
\end{frame}