| 1. | The properties of the existential quantifier are established by axioms.
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| 2. | This is equivalent to the TQBF using only existential quantifiers:
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| 3. | The let expression is a conjunction within an existential quantifier.
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| 4. | Existential quantifiers are dealt with by means of Skolemization.
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| 5. | The rule for existential quantifiers introduces new constant symbols.
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| 6. | Each set of axioms has but four existential quantifiers.
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| 7. | The above predicates contain the only existential quantifiers appearing in the entire proof.
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| 8. | The universal quantifier can be defined in terms of the existential quantifier and negation.
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| 9. | Variables not bound by an existential quantifier are bound by an implicit universal quantifier.
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| 10. | The possibility of this construction relies on the intuitionistic interpretation of the existential quantifier.
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