Axioms of Subsets

For any set theoretic formula f(x,t_1,t_2,...,t_n),

 ( 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 A there is a subset of A consisting exactly of those elements which satisfy the formula.

This entry contributed by Nicolas Bray

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Bray, Nicolas. "Axioms of Subsets." From MathWorld--A Wolfram Web Resource, created by Eric W. Weisstein.

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