	Let formula_12, and let "T" be any constructible subset of "S". Then there is some β with formula_13, so formula_14, for some formula Φ and some formula_15 drawn from formula_16. By the downward Löwenheim–Skolem theorem and Mostowski collapse, there must be some transitive set "K" containing formula_17 and some formula_18, and having the same first-order theory as formula_16 with the formula_18 substituted for the formula_15; and this "K" will have the same cardinal as formula_17. Since formula_23 is true in formula_16, it is also true in "K", so formula_25 for some γ having the same cardinal as α. And formula_26 because formula_16 and formula_28 have the same theory. So "T" is in fact in formula_29.