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Such Quantifier

Definition: term (such x: F)

• Takes variable x and formula F.
• Constructs term where x is bound.
• Value is some x such that F holds (if such an x exists).

New Axiom:

(exists x: F) => (forall x: x = (such x: F) => F),

If an object with property F exists, then the value of the "such term" satisfies F as well.