Axiom:Axiom of Replacement/Class Theory/Formulation 3

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Every mapping whose domain is a set is also a set.

Also known as

The axiom of replacement is also known as the axiom of substitution.

Also see

  • Results about the Axiom of Replacement can be found here.

Historical Note

The axiom of replacement was added to the axioms of Zermelo set theory by Abraham Halevi Fraenkel, and also independently by Thoralf Albert Skolem.

The resulting system of axiomatic set theory is now referred to as Zermelo-Fraenkel Set Theory.