(A) LEM is a $0$-premise rule in the system; thus, we have a $1$-line proof of :
$\vdash r \lor \lnot r$.
(B) $p \land q \to p$ is a tautology, thus it must be provable :
1) $p \land q$ --- assumed [a]
2) $p$ --- from 1) by $\land$-e
3) $\vdash p \land q \to p$ --- from 1) and 3) by $\to$-i, discharging [a].
Now, we can use the (obvious) property of the derivability relation : $\vdash \ $ [not present in the book; we can see it in : Dirk van Dalen, Logic and Structure (5th ed - 2013), page 37] :
if $\Gamma \vdash \varphi$, then $\Gamma \cup \Delta \vdash \varphi$,
to add to the above proofs the "unnecessary" premises, getting from (A) :
$p \land q \to p \vdash r \lor \lnot r$
and from (B) :
$r \lor \lnot r \vdash p \land q \to p$.
Now we can conclude with :
$p \land q \to p \dashv \vdash r \lor \lnot r$.