Proof
fun (A B X : Ens) (i : IN X A) (j : IN X B) =>
Set_Of_th1 A (fun U : Ens => IN U B) X i j.
Section intersection4.
Variable A B C : Ens.
Hypothesis s : SUB C A.
Hypothesis t : SUB C B.
Variable X : Ens.
Hypothesis i : IN X C.
Let step1 : IN X A.
Proof s X i.
Let step2 : IN X B.
Proof t X i.

Lemma intersection4_Out : IN X (intersection A B).
Proof intersection_th3 A B X step1 step2.