Axiom of Regularity

https://www.wikiwand.com/en/Axiom_of_regularity

Axiom of regularity or axiom of foundation states that every non-empty set $x$ contains a member $y$ such that $x$ and $y$ are disjoint sets.

$$\forall x[ \exists a(a\in x) \Rightarrow \exists y ( y\in x \land \lnot \exists z(z\in y\land z\in x) ) ]$$

This implies, for example, that no set is an element of itself and that every set has an ordinal rank.