We need two generalized tautologies involving implication. We need a law that says the conjunction of a set of propositions implies any one of the propositions. Intuitively, if we know all the p i are true we can conclude that any single one is true. Now for our proof that induction works. So, we examine those two cases.
G is a hypothesis.
G is a tautology. Thus, the right hand side must also be always TRUE and, hence, a tautology.