Existence of Tychonoff Space which is not Normal

Theorem
There exists at least one example of a topological space which is a Tychonoff space, but is not also a normal space.

Proof
Let $T$ be a Niemytzki's tangent disc space.

From Niemytzki's Tangent Disc Space is Tychonoff, $T$ is a Tychonoff space.

From Niemytzki's Tangent Disc Space is not Normal, $T$ is not a normal space.

Hence the result.