\begin{enumerate}
\item
Show that the following hold in the classical
propositional calculus:
\begin{enumerate}
\item
$Q \implies R \vdash (P \lor Q) \implies (P \lor R)$.
\item \label{PEIRCE}
$\vdash ((P \implies Q) \implies P) \implies P$.
\end{enumerate}
\item
Show that the following hold in classical first-order logic:
\begin{enumerate}
\item
$(\forall x) (Px \implies Qx)
\vdash (\forall x) Px \implies (\forall x) Qx$.
\item
$(\exists x)(\forall y) Pxy \vdash (\forall y)(\exists x) Pxy$.
\end{enumerate}
\end{enumerate}

