Questionnaire-2024/natural_deduction_propositional_logic/0042_sol.tex

\begin{center}
  \begin{minipage}{0.2\textwidth}
    \begin{prooftree}
      \AxiomC{$ \varphi$}
      \RightLabel{$ \ori1$}
      \UnaryInfC{$ \varphi \lor \psi$}
    \end{prooftree}
  \end{minipage}
  \begin{minipage}{0.2\textwidth}
    \begin{prooftree}
      \AxiomC{$ \varphi$}
      \RightLabel{$ \ori2$}
      \UnaryInfC{$ \psi \lor \varphi$}
    \end{prooftree}
  \end{minipage}
\end{center}

If we know that $\varphi$ holds, we can derive that $\varphi \lor \psi$ holds and that
$\psi \lor \varphi$ holds. This is true for any $\psi$.