\begin{frame}
  \frametitle{Rules for $\wedge$ and $\vee$}
  
  \begin{goal}{Introduction of $\wedge$}
    \vspace{-1ex}
    \begin{align*}
      \infer[\rulename{\wedge_i}]
      {\alpha \wedge \beta}
      {\alpha && \beta}
    \end{align*}
    (If you have derived $\alpha$ and $\beta$, then you can conclude $\alpha \wedge \beta$.)
  \end{goal}
  \pause
    
  \begin{goal}{Elimination of $\wedge$}
    \vspace{-1ex}
    \begin{align*}
      \infer[\rulename{\wedge_{e_1}}]
      {\alpha}
      {\alpha \wedge \beta}
      &&
      \infer[\rulename{\wedge_{e_2}}]
      {\beta}
      {\alpha \wedge \beta}
    \end{align*}
  \end{goal}
  \pause\medskip

  \begin{goal}{Rules for $\vee$}
    \vspace{-1ex}
    \begin{align*}
      \infer[\rulename{\vee_{i_1}}]
      {\alpha \vee \beta}
      {\alpha}
      &&
      \infer[\rulename{\vee_{i_2}}]
      {\alpha \vee \beta}
      {\beta}
    \end{align*}
  \end{goal}
\end{frame}