Point in Topological Space is Element of its Neighborhood

Theorem
Let $T = \left({S, \tau}\right)$ be a topological space.

Let $x \in S$.

Let $N$ be a neighborhood of $x$ in $T$.

Then $a \in N$.

That is:
 * $\forall x \in S: \forall N \in \mathcal N_x: x \in N$

where $\mathcal N_x$ is the neighborhood filter of $x$.

Proof
Trivially follows by definition of neighborhood of $a$.