\begin{proof} \begin{enumerate} \item \begin{align*} (\Theta \circ \Psi)\circ\Phi & = \{(w,z)\mid (w,x)\in\Phi\text{ and }(x,z)\in\Theta\circ\Psi\text{ for some }x\} \\ & = \{(w,z)\mid(w,x)\in\Phi\text{ and }(x,y)\in\Psi\text{ and }(y,z)\in\Theta\text{ for some }x,y\} \\ & = \{(w,z)\mid(w,y)\in\Psi\circ\Phi\text{ and }(y,z)\in\Theta\text{ for some }y\} \\ & = \Theta\circ(\Psi\circ\Phi). \end{align*}
\item x
\item x
\end{enumerate} \end{proof}