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Section union_th1_proof.
Variable A : Ens.
Variable B : Ens.
Let U := union A B.
Variable X : Ens.
Hypothesis h : IN X A.
Let step1 : SUB A U.
Proof union_pr1 A B.
Definition union_th1_Out : IN X U := step1 X h.
End union_th1_proof.

Theorem union_th1 : forall (A B X : Ens) (h : IN X A), IN X (union A B).
Proof union_th1_Out.