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.
Proof intersection_th3 A B X step1 step2.
End intersection4.

Theorem intersection_th4 :
forall (A B C : Ens) (s : SUB C A) (t : SUB C B), SUB C (intersection A B).