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.
Proof EQ_symm (EV F X) (EV G X) step1.
End ee_symm_proof.

Theorem ex_eq_symm :
forall F G : Ens,
Extensionally_equivalent F G -> Extensionally_equivalent G F.