The universal class is the class of all sets:
\[\V = \{x : x = x\}.\]
$\V$ is a proper class.
Proof. Since $\V = \V$, it follows that $\V \in \V$, contrary to irreflexivity of $\in$.
The universal class is the class of all sets:
\[\V = \{x : x = x\}.\]
$\V$ is a proper class.
Proof. Since $\V = \V$, it follows that $\V \in \V$, contrary to irreflexivity of $\in$.