intros a; apply I1.
exists a; auto with zfc.
intros a'; cut (EXType A (fun x : A => EQ (f' a') (f x))).
simple induction 1; intros a ea; exists a; auto with zfc.
apply I2; exists a'; auto with zfc.
Qed.
Hint Resolve INC_EQ: zfc.
(* Membership is extentional (i.e. is stable w.r.t. EQ)   *)

(* Specifications: *)
Theorem IN_sound_left :
forall E E' E'' : Ens, EQ E E' -> IN E E'' -> IN E' E''.
Theorem IN_sound_left :
forall E E' E'' : Ens, EQ E E' -> IN E E'' -> IN E' E''.