Note 480 — Chapter I
Reading edition
It may assist the reader in following the reasoning in section 427 if we work through this particular case independently. If AA = A, then aa = a, for whatever is formally valid in the case of A must also be formally valid in the case of any other term. But if two terms are equivalent their contradictories must be equivalent. Hence from aa = a, it follows that A or A = A. And it is clear that we might pass similarly from A or A = A to AA = A.