Simplify Propositional Form I was solving this problem.
Simplify propositional form:
 $$[(p\implies q) \vee (p \implies r)] \implies (q \vee r)$$
I was using this fact for solving:
$$(p \implies q) \equiv (\neg p \vee q)$$
but end up with
$$(p \implies (q \vee r)) \implies (q \vee r)$$
I need help to further simplifying this expression. Any kind of help would be appreciated. Thanks!

HINT. If looking for a simpler expression:
$$
((p\implies q) \lor (p \implies r)) \implies (q \lor r) \\
 \equiv  \lnot((\lnot p \lor q) \lor (\lnot p \lor r)) \lor (q \lor r) \\
 \equiv  \lnot(\lnot p \lor q \lor r) \lor (q \lor r) \\
 \equiv  ( p \land \lnot (q \lor r)) \lor (q \lor r)\\
 \equiv  ( p \lor q \lor r ) \land (\lnot (q \lor r) \lor (q \lor r)) \\
 \equiv  p \lor q \lor r  
$$
