Is ∃x.ϕ defined as ¬∀x.¬ϕ, since the axioms don't mention ∃? Do you have any previously derived theorems about ∃, such as ? Also, are you allowed to use the deduction theorem?
Hi, I have no idea how to begin constructing this proof, and I would appreciate any help!
I need to prove the following, and to make matters worse, without soundness or completeness
⊢ (∀x.ϕ) →(∃x.ϕ)
I can use the following axioms/theorems http://img233.imageshack.us/img233/5...11115at824.png Thank you.
Please note that any sort of help to get me started on the proof would be very helpful.
Is ∃x.ϕ defined as ¬∀x.¬ϕ, since the axioms don't mention ∃? Do you have any previously derived theorems about ∃, such as ? Also, are you allowed to use the deduction theorem?