Proof power4_Out.
Section power5.
Variable A B : Ens.
Hypothesis a : SUB A B.
Variable X : Ens.
Hypothesis x : IN X (Powerset A).
Let step1 : SUB X A.
Proof Powerset_pr2 A X x.
Let step2 : SUB X B.
Proof SUB_trans X A B step1 a.

Lemma power5_Out : IN X (Powerset B).
Proof Powerset_pr1 B X step2.