Consider NFU set theory as presented in this: http://math.boisestate.edu/~holmes/holmes/head.pdf
On page 15 of that pdf it states that the following is an axiom: The set $\{X\colon X=X\}$ exists.
Let $V = \{X\colon X=X\}$.
$V$ is an element of $V$ as $V=V$.
How is this not circular?