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

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


 * $(5)\quad $every open cover of $T$ has an open $\sigma$-discrete refinement
 * $(6)\quad $every open cover of $T$ has an open $\sigma$-locally finite refinement

Proof

 * $(5)\quad $every open cover of $T$ has an open $\sigma$-discrete refinement
 * $\cdots$
 * $(6)\quad $every open cover of $T$ has an open $\sigma$-locally finite refinement