Proof
fun (R Y : Ens) (p : Range_prop R Y) =>
CHOICE_pr (fun X : Ens => IN (PAIR X Y) R) p.
(*********** boundedness for Domain_prop and Range_prop ******)
Section Domain_prop_bounded_proof.
Variable R : Ens.
Let T := Total R.
Section Domain_prop_bounded_proof_1.
Variable X : Ens.
Hypothesis p : Domain_prop R X.
Let Y := EV R X.
Let step1_1 : IN (PAIR X Y) R.
Proof EV_pr R X p.

(* Specifications: *)
Lemma Domain_prop_bounded_proof_1_Out : IN X T.
Proof Relation_Total_th1 R X Y step1_1.