The residue theorem
Let $\Omega\subseteq \mathbb{C}$ open, $f$ meromorphic on $\Omega$ and $A$ be the set of the poles of $f$. If $\Gamma$ is a cycle in $\Omega\backslash A$ with $\mathrm{ind}_{\Gamma}(\alpha)=0$ for $\alpha\in \mathbb{C}\backslash \Omega$, we have: $ \frac{1}{2\pi i}\int_{\Gamma}f(z)\mathrm{d}z=\sum_{a\in A}{\rm Res}(f,\ a)\cdot \mathrm{ind}_{\Gamma}(a) $
Usually, there is a sketch of the proof on wikipedia. But, there isn't one for this theorem. Can someone point me or explain me an outline of the proof to this one? Just the most important steps.