Editing Axiom of regularity (section)

=== For every two sets, only one can be an element of the other ===
Let ''X'' and ''Y'' be sets. Then apply the axiom of regularity to the set {''X'',''Y''} (which exists by the axiom of pairing). We see there must be an element of {''X'',''Y''} which is also disjoint from it. It must be either ''X'' or ''Y''. By the definition of disjoint then, we must have either ''Y'' is not an element of ''X'' or vice versa.