T3 Lindelöf Space is Fully T4 Space

Theorem
Let $T = \struct {S, \tau}$ be a $T_3$ Lindelöf topological space.

Then:
 * $T$ is a fully $T_4$ space

Proof
From Lindelöf T3 Space is Paracompact:
 * $T$ is a paracompact space

From T3 Space is Fully T4 iff Paracompact:
 * $T$ is a fully $T_4$ space