\begin{proposition}\label{first_proposition}
    $a = a$.
\end{proposition}

\begin{proposition}\label{second_proposition}
    $b = b$.
\end{proposition}

\begin{proposition}\label{third_proposition}
    $c = c$.
\end{proposition}
\begin{proof}
    Follows by \ref{first_proposition}. % Should filter out second_proposition
\end{proof}

\begin{proposition}\label{fourth_proposition}
    $e = e$.
\end{proposition}
\begin{proof}
    For all $d$ we have $d = d$ by \ref{first_proposition}.
\end{proof}

\begin{proposition}\label{fifth_proposition}
    $f = f$.
\end{proposition}