by the induction hypothesis, hence we can infer This completes the proof of .Now let F be a tautology in variables p₁, ..., p_n. We will prove by reverse induction on k = n,...,0 that for every assignment e,The base case k = n follows from a special case of using
:and the fact that F->F is a theorem by the deduction theorem.

Assume that holds for k + 1, we will show it for k. By applying deduction theorem to the induction hypothesis, we obtain
:by first setting e(p_k+1) = 0 and second setting