Characterization of Paracompactness in T3 Space/Statement 3 implies Statement 4

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


 * $(3)\quad $every open cover of $T$ has a closed locally finite refinement
 * $(4)\quad $every open cover of $T$ is even

Proof

 * $(3)\quad $every open cover of $T$ has a closed locally finite refinement
 * $\cdots$
 * $(4)\quad $every open cover of $T$ is even