Let $\Omega \subseteq \mathbb{C}$ be a D4898: Complex domain such that

(i)	\begin{equation} \Omega \neq \emptyset \end{equation}
(ii)	$f : \Omega \to \mathbb{C}$ is a D1392: Holomorphic function on $\Omega$
(iii)	\begin{equation} \exists \, z, w \in \Omega : z \neq w \text{ and } f(z) \neq f(w) \end{equation}

Then \begin{equation} \max_{z \in \Omega} |f(z)| = \emptyset \end{equation}