Editing Axiom of pairing (section)

=== Non-independence ===
The axiom of pairing is generally considered uncontroversial, and it or an equivalent appears in just about any [[axiomatization]] of set theory. Nevertheless, in the standard formulation of the [[Zermelo–Fraenkel set theory]], the axiom of pairing follows from the [[axiom schema of replacement]] applied to any given set with two or more elements, and thus it is sometimes omitted. The existence of such a set with two elements, such as { {}, { {} } }, can be deduced either from the [[axiom of empty set]] and the [[axiom of power set]] or from the [[axiom of infinity]].

In the absence of some of the stronger ZFC axioms, the axiom of pairing can still, without loss, be introduced in weaker forms.