A new proof of the compactness theorem for propositional logic

The compactness theorem for propositional logic states that a demumerable set of propositional formulas is satisfiable if every finite subset is satisfiable. Though there are many different proofs, the underlying combinatorial basis of most of them seems to be Kόnig's lemma on infinite trees (see Smullyan [2], Thomson [3]). We base our proof on a different combinatorial lemma due to R. Rado [1], which allows us to easily prove a more general compactness theorem, viz., a well-ordered set of propositional formulas is satisfiable if every finite subset is (one gets a non-denumerable set of formulas, by allowing non-denumerably many propositional variables).