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+\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}