Section power3.
Variable A X Y : Ens.
Hypothesis x : IN X A.
Hypothesis y : IN Y A.
Let step1 : IN (Singleton X) (Powerset A).
Proof Powerset_th4 A X x.
Let step2 : IN (Singleton Y) (Powerset A).
Proof Powerset_th4 A Y y.
Proof Powerset_th2 A (Singleton X) (Singleton Y) step1 step2.
End power3.

Theorem Powerset_th5 :
forall (A X Y : Ens) (x : IN X A) (y : IN Y A),
IN (Doubleton X Y) (Powerset A).