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}