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Universal Quantifier ∀

A formula that uses a universal quantifier expresses that a particular property holds for all possibles values.
For example, (A. x (= (+ x (5)) (+ (5) x))) means that (= (+ x (5)) (+ (5) x)) is true for all possible values of x. Universal quantifiers are part
of Predicate Calculus.

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Axioms

The properties of the universal quantifier are derived directly from the the axioms of predicate calculus.

Predicate calculus