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Uniqueness Quantifier ∃!

A formula that uses a uniqueness quantifier expresses that there exists one and only one number with a particular property.
For example, (E! x (= (* (2) x) (6))) means that there exists some number x for which (= (* (2) x) (6)) and no other numbers satisfy this property.
Uniqueness quantifiers are part of predicate calculus.

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Definition

The uniqueness quantifier is defined as (<-> (E! x ph) (E. y (A. x (<-> ph (= x y))))) /edit/peano_new/predicate/equality.gh/df-eu.

Predicate calculus