# Proof of Liouville's Theorem for Harmonic functions

Recall that a function $f:U (\subset \mathbb R^2) \to \mathbb R$ is called harmonic if $\Delta f=0$ where $\Delta$ is Laplacian operator.

Liouville's Theorem: Let $f$ be a harmonic and bounded function then $f$ is constant.( I know that harmonic functions have mean value property)

I know that harmonic functions have mean value property,how can i deduce Liouville's theorem using mean value property and maximum modulus principle.