Let step4 : SUB (intersection X Y) X.
Proof intersection_th1 X Y.
Let step5 : SUB (intersection X Y) A.
Proof SUB_trans (intersection X Y) X A step4 step1.

(* Specifications: *)
Lemma power1_Out2 : IN (intersection X Y) (Powerset A).
Proof Powerset_pr1 A (intersection X Y) step5.