Axiom
relational_choice :
forall (A B:Type) (R:A -> B -> Prop),
(forall x:A, exists y : B, R x y) ->
exists R' : A -> B -> Prop,
(forall x:A,
exists y : B,
R x y /\ R' x y /\ (forall y':B, R' x y' -> y = y')).