## Uniform Convergence

Hi!

Let $G \in \mathbb{C}$ be a bounded domain and let $f_n$ be a sequence of functions that are holomorphic on $G$ and continuous on $\overline{G}$. Show that if $f_n$ converges uniformly on $\partial G$, then it converges uniformly on $\overline{G}$ as well.

I think one has to use Montel's theorem, but I dont know...