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.
Proof Powerset_pr1 B X step2.
End power5.

Theorem Powerset_th7 :
forall (A B : Ens) (a : SUB A B), SUB (Powerset A) (Powerset B).