Identity of Group is in Singleton Conjugacy Class

Theorem
Let $G$ be a group.

Let $e$ be the identity of $G$.

Then $e$ is in its own singleton conjugacy class:
 * $\conjclass e = \set e$

Proof
From Identity of Group is in Center:
 * $e \in \map Z G$

where $\map Z G$ is the center of $G$.

From Conjugacy Class of Element of Center is Singleton:
 * $\conjclass e = \set e$