The universal class / universe 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 PROP-ZF-SLF.
The universal class / universe 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 PROP-ZF-SLF.