stylistic:tone, stylistic:style_transfer
Axiom of pairing

If x {\displaystyle x} and y {\displaystyle y} are sets, then there exists a set which contains x {\displaystyle x} and y {\displaystyle y} as elements, for example if x = {1,2} and y = {2,3} then z will be {{1,2},{2,3}}

The axiom schema of specification must be used to reduce this to a set with exactly these two elements. The axiom of pairing is part of Z, but is redundant in ZF because it follows from the axiom schema of replacement if we are given a set with at least two elements. The existence of a set with at least two elements is assured by either the axiom of infinity, or by the axiom schema of specification and the axiom of the power set applied twice to any set.