Mean value property

Statement

Let $U \subseteq \mathbb{C}$ be an open set, and identify $\mathbb{C}$ with $\mathbb{R}^2$ by $x + iy \leftrightarrow (x, y)$. Let $u : U \to \mathbb{R}$ be harmonic: $u$ is twice continuously differentiable and $u_{xx} + u_{yy} = 0$ on $U$. Let $c \in \mathbb{C}$ and $r > 0$ be such that the closed disc $\{z : |z - c| \le r\}$ is contained in $U$. Then $$u(c) = \frac{1}{2\pi} \int_0^{2\pi} u(c + r e^{i\theta}) \, d\theta.$$