Riemann's removable singularity theorem

Let \(\Omega\subseteq\CC\) be open, let \(z_0\in\Omega\), and let \(f\) be holomorphic on \(\Omega\setminus\{z_0\}\) and bounded on \(\Omega\setminus\{z_0\}\). Then \(z_0\) is a removable singularity of \(f\): \(f\) extends to a holomorphic function on \(\Omega\).