% John David Stone
% Department of Mathematics and Computer Science
% Grinnell College
% stone@cs.grinnell.edu

% created June 19, 2002
% last revised June 21, 2002

\documentclass[11pt]{article}

\begin{document}
\newtheorem{theorem}{Theorem}
\begin{theorem}
For any sets $A$ and $B$, $(\wp A) \cup (\wp B) \subseteq \wp (A \cup B)$.
\end{theorem}

\textsc{proof.}
\begin{eqnarray*}
C \in (\wp A) \cup (\wp B)
  & \longleftrightarrow & C \in \wp A \,\vee\, C \in \wp B \\
  & \longleftrightarrow & C \subseteq A \,\vee\, C \subseteq B \\
  & \longrightarrow & C \subseteq A \cup B \\
  & \longrightarrow & C \in \wp (A \cup B).
\end{eqnarray*}
\end{document}