T3 Space with Sigma-Locally Finite Basis is T4 Space/Proof 2

Proof
From User:Leigh.Samphier/Topology/T3 Space with Sigma-Locally Finite Basis is Paracompact:
 * $T$ is a paracompact space

From $T_3$ Space is Fully $T_4$ iff Paracompact:
 * $T$ is a fully $T_4$ space.

From Fully $T_4$ Space is $T_4$ Space:
 * $T$ is a $T_4$ space.