Section EXISTS_th1_proof.
Variable P : Ens -> Prop.
Variable X : Ens.
Hypothesis p : P X.
Hypothesis h : DOESNT_EXIST P.
Let step1 : ~ P X.
Proof h X.
Proof step1 p.
End EXISTS_th1_proof.

Theorem EXISTS_th1 : forall (P : Ens -> Prop) (X : Ens) (p : P X), EXISTS P.