Section union_th2_proof.
Variable A : Ens.
Variable B : Ens.
Let U := union A B.
Variable X : Ens.
Hypothesis h : IN X B.
Let step1 : SUB B U.
Proof union_pr2 A B.
Definition union_th2_Out : IN X U := step1 X h.
End union_th2_proof.

Theorem union_th2 : forall (A B X : Ens) (h : IN X B), IN X (union A B).