unfold inter in |- *.
intros.
elim H; clear H; intros H Ht; elim Ht; clear Ht; intros H1 H2.
red in |- *; intro.
cut (dans x empty); auto.
intro.
apply dans_empty_imp_P with x; auto.
Qed.

Lemma sym_inter : forall A B C : Ensf, inter A B C -> inter B A C.
unfold inter in |- *.