Reduction To Ordinary Existential and Universal Quantification
Uniqueness quantification can be expressed in terms of the existential and universal quantifiers of predicate logic by defining the formula ∃!x P(x) to mean
where an equivalence is:
An equivalent definition that has the virtue of separating the notions of existence and uniqueness into two clauses, at the expense of brevity, is
Another equivalent definition with the advantage of brevity is
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