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Quantifier proof Question

  1. Nov 15, 2011 #1
    Hello, I have no idea how to solve this proof and would actually appreciate your help. I cannot use soundness or completeness.

    ⊢ (∀x.ϕ) →(∃x.ϕ)

  2. jcsd
  3. Nov 15, 2011 #2


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    It will depend on the particular deductive apparatus. You might be using a set of axioms together with a set of rules of inference, or you might be using a system of natural deduction, etc. Let's suppose it's a natural deduction system.

    Assume your antecedent. Often you will have a rule of universal instantiation that allows you to go from the assumed antecedent to an instance, then a rule that lets you go from the instance to the existential generalization of the instance (which is the consequent). Then an application of conditionalization gets you home. Does that help?
    Last edited: Nov 15, 2011
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