, and so on; then
,
,
, ... is a progression, and is a sub-class of
. Assuming the multiplicative axiom, such a selection can be made. Thus by twice using this axiom we can prove that, if the axiom is true, every non-inductive cardinal must be reflexive. This could also be deduced from Zermelo's theorem, that, if the axiom is true, every class can be well ordered; for a well-ordered series must have either a finite or a reflexive number of terms in its field.