By extensionality, the product by formula_88 axiom implies the existence of a unique class, which is denoted by formula_107 This axiom is used to define the class formula_108 of all : formula_109 and formula_110 If formula_19 is a class, extensionality implies that formula_112 is the unique class consisting of the of formula_113 For example, the membership axiom produces a class formula_61 that may contain elements that are not ordered pairs, while the intersection formula_115 contains only the ordered pairs of formula_61.