2
$\begingroup$

Possible Duplicate:
First order logic proof question

I need to prove this: ⊢ (∀x.ϕ) →(∃x.ϕ)

Using the following axioms: http://img233.imageshack.us/img233/5846/screenshot20111115at824.png

The only thing I did was use deduction theorem: (∀x.ϕ) ⊢(∃x.ϕ)

And then changed (∃x.ϕ) into (~∀x.~ϕ), so: (∀x.ϕ) ⊢ (~∀x.~ϕ)

How can I continue with this? I cannot use soundness/completeness theorems.

EDIT: ∀* means it is a finite sequence of universal quantifiers (possible 0)

1 Answers 1