State and prove the Completeness Theorem for Propositional Logic. [You do not need to give definitions of the various terms involved. You may assume that the set of primitive propositions is countable. You may also assume the Deduction Theorem, provided that you state it clearly.]

Where in your argument have you used the third axiom, namely $(\neg \neg p) \Rightarrow p ?$

State the Compactness Theorem, and deduce it from the Completeness Theorem.