Axiom schema of replacement
![Axiom schema of replacement: the image F[A] of the domain set A under the definable class function F is itself a set, B.](/Images/godic/202412/22/Axiom_schema_of_replacement.svg0408.png")
![Axiom schema of collection: the image f[A] of the domain set A under the definable class function f falls inside a set B.](/Images/godic/202412/22/Codomain2_A_B.SVG0408.png")
In set theory, the axiom schema of replacement is a schema of axioms in Zermelo–Fraenkel set theory (ZFC) that asserts that the image of any set under any definable mapping is also a set. It is necessary for the construction of certain infinite sets in ZFC.