Editing Axiom of regularity (section)

===No set is an element of itself===
Let ''A'' be a set, and apply the axiom of regularity to {''A''}, which is a set by the [[axiom of pairing]]. We see that there must be an element of {''A''} which is disjoint from {''A''}. Since the only element of {''A''} is ''A'', it must be that ''A'' is disjoint from {''A''}. So, since <math display="inline">A \cap \{A\} = \varnothing</math>, we cannot have ''A''  an element of ''A'' (by the definition of [[Disjoint sets|disjoint]]).