Substitutions into propositional tautologies

We prove that there is a polynomial time substitution (y1,…,yn):=g(x1,…,xk) with k≪n such that whenever the substitution instance A(g(x1,…,xk)) of a 3DNF formula A(y1,…,yn) has a short resolution proof it follows that A(y1,…,yn) is a tautology. The qualification “short” depends on the parameters k and n.