This is actually weaker than the full axiom of choice, but you can still show that no such object is computable.
Presumably this is an ever-present hazard in any proof using the axiom of choice - in this case it is relatively obvious, but how easy is it to accidentally rely on such an uncomputable object in a dusty corner of your proof?
Presumably this is an ever-present hazard in any proof using the axiom of choice - in this case it is relatively obvious, but how easy is it to accidentally rely on such an uncomputable object in a dusty corner of your proof?