Let $G \subset \mathbb{C}$ be a simply connected region and $f, g$ be two analytic functions defined on $G$ with $f \left( G ight) = g \left( G ight) = \Omega \subset \mathbb{C}$. Let $f, g$ be invertible with analytic inverse. Suppose that there are two points $z_1, z_2 \in G$, $z_1 eq z_2$ such that $f \left( z_1 ight) = g \left( z_1 ight)$ and $f \left( z_2 ight) = g \left( z_2 ight)$. We wish to show that $f \equiv g$