 Also in classical mathematics the choice axioms are treated with care, and it is often explicitly mentioned how much choice is needed in a proof. Since the axiom of dependent choice is consistent with an important axiom in classical set theory (the axiom of determinacy) while the full axiom of choice is not, special attention is payed to this axiom and in general one tries to reduce the amount of choice in a proof, if choice is present at all, to dependent choice. 