\begin{abbreviation}\label{phase5_quantified_identity}
    The phase five quantified identity of $A$ is $A$.
\end{abbreviation}

\begin{abbreviation}\label{phase5_quantified_contains}
    $A$ contains $B$ iff $B\in A$.
\end{abbreviation}

\begin{proposition}\label{phase5_quantified_function_argument}
    The phase five quantified identity of every set $A$ is equal to $A$.
\end{proposition}
\begin{proof}
    Follows.
\end{proof}

\begin{proposition}\label{phase5_quantified_verb_argument}
    Let $A$ be a set.
    Then $A$ contains every element of $A$.
\end{proposition}
\begin{proof}
    Follows.
\end{proof}