Hi all. I just started uni a week ago, so I'm very new at this subject, please try and help me understand it

I need to prove that ((p->q)^(q->r))->(p->r) or in other words, if p implies q, and q implies r, p implies r.

I need to prove this without using a truth table. Just expand the implications of ((p->q)^(q->r)) like an equation and get ((not p)vr) which is equivalent to p->r