and

is the number of collections of sub-classes, then, provided

is not inductive,

must be reflexive. But this is a long way from what we set out to prove.

In order to advance beyond this point, we must employ the multiplicative axiom. From each set of sub-classes let us choose out one, omitting the sub-class consisting of the null-class alone. That is to say, we select one sub-class containing one term,