Proof of the Hopf Lemma for Elliptic Equations.

Question

I would like some help to understand the Hopf Lemma, i do not understand this part:

Indeed, we may find $\delta$ so that $u(x)<u(x_{0})-\delta$ for $x \in \partial \Sigma\cap B$. Take $\epsilon$ so that $\epsilon h <\delta$ on $\partial \Sigma\cap B$, then $w(x)<u(x_{0})=w(x_{0})$ for all $ x \in \partial \Sigma\cap B$

Thanks for the help!