Stuck up on something in complex analysis.
Let $f$ analytic function and open $\Omega \subset \mathbb{C}$. Show that if $f$ is not a constant on a neighbourhood of $z_0$, then exist a neighbourhood $V$ of $z_0$ so that
$z\in \mathbb{V}$ and $f(z)=f(z_0) \Rightarrow z=z_0$.
Note: This should be proven without Cauchy-Riemann because of the axiomatic system of the book.