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    The formula ∀y(y ∈ x → y ∈ a) is true only of sets by the... — Carmelics
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    Home/Proof of definition segments
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    Supports→The Power Set axiom is true for sets.

    The formula ∀y(y ∈ x → y ∈ a) is true only of sets by the Axiom of Subsets.

    All sources support itProof of definition segments
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    Proof of definition segmentsAll sources support it

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    Philosophy of Language2 linked

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    Related propositions within the same area of thought.
    The Power Set axiom is true for sets.The formula ∀y(y ∈ x → y ∈ a) has only the set a as a parameter.The formula ∀y(y ∈ x → y ∈ a), where a is a set, does not mention sethood.

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    The formula ∀y(y ∈ x → y ∈ a) has only the set a as a parameter.90%The formula ∀y(y ∈ x → y ∈ a), where a is a set, does not mention seth...89%The formula is true only of sets88%The formula ∃y(x ∈ y ∧ y ∈ a), where a is a set, does not mention seth...84%

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    SEP: settheory-alternative
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    The formula \(\forall y(y \in x \rightarrow y \in a)\), where \(a\) is a set, does not mention sethood, has only the set \(a\) as a parameter, and is true only of sets by the Axiom of Subsets. Thus Power Set is true for sets.

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