Section ee_symm_proof.
Variable F G : Ens.
Hypothesis e : Extensionally_equivalent F G.
Variable X : Ens.
Hypothesis i : IN X (Domain G).
Hypothesis j : IN X (Domain F).
Let step1 : EQ (EV F X) (EV G X).
Proof e X j i.

Lemma ee_symm_Out : EQ (EV G X) (EV F X).