Editing Axiom schema of replacement (section)

=== Simplifications ===
Some simplifications may be made to the axiom schema of replacement to obtain different equivalent versions. [[Azriel Lévy]] showed that a version of replacement with parameters removed, i.e. the following schema, is equivalent to the original form. In particular the equivalence holds in the presence of the axioms of extensionality, pairing, union and powerset.<ref>A. Kanamori, "[https://math.bu.edu/people/aki/20.pdf In Praise of Replacement]", pp.74--75. Bulletin of Symbolic Logic vol. 18, no. 1 (2012). Accessed 22 August 2023.</ref>

: <math>\forall A \, ( [ \forall x \, \exists ! y \, \phi(x, y, A) ]\ \Longrightarrow\ \exists B \, \forall y \, [y \in B \Leftrightarrow \exists x \in A \, \phi(x, y, A) ] )</math>