Section Singleton_th2_proof.
Variable X : Ens.
Let B := Singleton X.
Let step1 : IN X B. Proof Singleton_pr1 X.
Hypothesis h : Its_empty B.
Let step2 : IN X B -> False.
Proof h X.
Definition Singleton_th2_proof_Out : False := step2 step1.
End Singleton_th2_proof.

Theorem Singleton_th2 : forall X : Ens, Its_nonempty (Singleton X).
Proof Singleton_th2_proof_Out.