Section Domain_th1_proof.
Variable R : Ens.
Variable X Y : Ens.
Hypothesis i : IN (PAIR X Y) R.
Let step1 : Domain_prop R X.
Proof EXISTS_th1 (fun Y1 : Ens => IN (PAIR X Y1) R) Y i.
Proof Domain_pr1 R X step1.
End Domain_th1_proof.

Theorem Domain_th1 :
forall (R X Y : Ens) (i : IN (PAIR X Y) R), IN X (Domain R).