Characterization of Paracompactness in T3 Space/Statement 1 implies Statement 2

Theorem
Let $T = \struct{X, \tau}$ be a $T_3$ Space.


 * $(1)\quad T$ is paracompact
 * $(2)\quad $every open cover of $T$ has a locally finite refinement

Proof

 * $(1)\quad T$ is paracompact
 * $\cdots$
 * $(2)\quad $every open cover of $T$ has a locally finite refinement