\begin{frame}
  \frametitle{Other Important Facts}

  \begin{block}{}
    \vspace{-1.5ex}
    \begin{talign}
      \alpha \models \beta \quad\iff\quad \models \alpha \to \beta
    \end{talign}
  \end{block}
  \pause
  
  \begin{block}{}
    \vspace{-1.5ex}
    \begin{talign}
      \alpha_1,\ldots,\alpha_n \models \beta \quad\iff\quad \alpha_1,\ldots,\alpha_{n-1} \models \alpha_{n} \to \beta
    \end{talign}
  \end{block}
  \pause
  
  \begin{block}{}
    \vspace{-1.5ex}
    \begin{talign}
      \alpha_1,\ldots,\alpha_n \models \beta \quad\iff\quad \models \alpha_1 \to (\alpha_2 \to (\ldots (\alpha_{n} \to \beta) \ldots))
    \end{talign}
  \end{block}
  \pause\bigskip
  
  \begin{block}{}
    \vspace{-1.5ex}
    \begin{talign}
      \models \alpha \wedge \beta \quad\iff\quad \models \alpha \;\text{ and }\; \models \beta
    \end{talign}
  \end{block}
  \pause
  
  \begin{block}{}
    \vspace{-1.5ex}
    \begin{talign}
      \models \alpha \;\text{ or }\; \models \beta \quad\implies\quad \models \alpha \vee \beta 
    \end{talign}
  \end{block}
  \pause

  \begin{alertgoal}{}
    \vspace{-1.5ex}
    \begin{talign}
      \models \alpha \vee \beta \quad\nimplies\quad   \models \alpha \;\text{ or }\; \models \beta 
    \end{talign}
    \pause    
    For example: $\models p \vee \neg p$, but not $\models p$ and not $\models \neg p$.
  \end{alertgoal}
\end{frame}