1. Given: Each consistent sentence (from which you cannot derive a contradiction) is satisfiable (true in some denumerable model).
<br>2. Every sentence that is not satisfiable (false in every model) is inconsistent (a contradiction may be derived from it).
<br>3. If sentence S is true then:<ul>
<li>S is satisfied in every model (by definition of ‘true’),
<li>¬S is false in every model.
<li>A contradiction can be derived from ¬S.
(See (2.) above.)
<li>The derivation of the contradiction constitutes a reductio ad absurdum proof of S.
<li>There is a proof of S.</ul>
We have thus shown that any true sentence is provable.