Characterization of Paracompactness in T3 Space/Statement 5 implies Statement 6

Theorem
Let $T = \struct{X, \tau}$ be a topological space.

If every open cover of $T$ has an open $\sigma$-discrete refinement then:


 * every open cover of $T$ has an open $\sigma$-locally finite refinement

Proof
Follows immediately from Sigma-Discrete Set of Subsets is Sigma-Locally Finite.