Graph of Continuous Mapping to Hausdorff Space is Closed in Product

Theorem
Let $T_A = \struct {S_A, \tau_A}$ and $T_B = \struct {S_B, \tau_B}$ be topological spaces.

Let $T_B$ be a Hausdorff space.

Let $f: T_A \to T_B$ be a continuous mapping.

Then the graph of $f$ is a closed subset of $T_A \times T_B$ under the product topology.

Proof
Let $G_f$ be the graph of $f$:
 * $G_f = \set {\tuple {s, t} \in S_A \times S_B: \map f s = t}$