Section Range_th1_proof.
Variable R : Ens.
Variable X Y : Ens.
Hypothesis i : IN (PAIR X Y) R.
Let step1 : Range_prop R Y.
Proof EXISTS_th1 (fun X1 : Ens => IN (PAIR X1 Y) R) X i.
Proof Range_pr1 R Y step1.
End Range_th1_proof.

Theorem Range_th1 :
forall (R X Y : Ens) (i : IN (PAIR X Y) R), IN Y (Range R).