real analysis - $sigma$-finite measure and semi-finite measure

Let $(X, \Sigma, \mu)$ it will be a space with measure.

$\mu$ is $\sigma$-finite measure if it exist sequence of sets $X_{i} \in \Sigma$ and $\cup_{i=1}^{\infty}X_{i}=X$ and $\mu(X_{i})<\infty$ for all i

$\mu$ is semi-finite measure if for all $G \in \Sigma$ and $\mu (G)=\infty$ it exist $H \in \Sigma$ and $H \subset G$ and $0<\mu(H)<\infty$

Show that if $\mu$ is $\sigma$-finite measure then $\mu$ is semi-finite measure