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    Any formula that does not mention sethood, has only sets ... — Carmelics
    Home/Proof of definition segments
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    Supports→The Axiom of Pairing is true for sets

    Any formula that does not mention sethood, has only sets as parameters, and is true only of sets, defines a set

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    Proof of definition segmentsAll sources support it

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    The Axiom of Pairing is true for setsThe formula has only the sets a and b as parametersThe formula is true only of setsThe formula x = a ∨ x = b (where a and b are sets) does not mention sethood

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    The formula ∃y(x ∈ y ∧ y ∈ a), where a is a set, does not mention seth...89%The formula ∀y(y ∈ x → y ∈ a), where a is a set, does not mention seth...87%The formula is true only of sets85%The formula x = a ∨ x = b (where a and b are sets) does not mention se...85%

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    The formula \(x = a \lor x = b\) (where \(a\) and \(b\) are sets) does not mention sethood, has only the sets \(a\) and \(b\) as parameters, and is true only of sets. Thus it defines a set, and Pairing is true for sets.

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