Axioms of Subsets

For any set theoretic formula ,

( forall t_1)( forall t_2)...( forall t_n)( forall A)( exists B)( forall x)(x in B <==> x in A ^ f(x,t_1,...,t_n)).

In other words, for any formula and set there is a subset of consisting exactly of those elements which satisfy the formula.

This entry contributed by Nicolas Bray

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Weisstein, Eric W., with contributions by Nicolas Bray. "Axioms of Subsets." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/AxiomsofSubsets.html

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