Justification

For idempotence: to be an *a* which is an *a* is the same thing as to be an *a*

For commutativity: to be an *a* which is a *b* is the same thing as to be a *b* which is an *a*

For associativity: to be an *a* which is a (*b* which is a *c*) is the same thing as to be an (*a* which is a *b*) which is a *c*.

for = and ' DN *<sup>a</sup>*"= *a* (Term Double Negation)
