# Basic Universe is Supercomplete

## Theorem

Let $V$ be a basic universe.

Then $V$ is supercomplete.

## Proof

By definition, a class $V$ is supercomplete if and only if $V$ is both transitive and swelled.

From the Axiom of Transitivity, $V$ is transitive.

From the Axiom of Swelledness, $V$ is swelled.

Hence the result.

$\blacksquare$