Section ieieep2.
Variable X : Ens.
Hypothesis i : IN X EmptySet.
Let step2_1 : False.
Proof EmptySet_th1 X i.
Proof false_implies_everything (IN X A) step2_1.
End ieieep2.
Let step2 : SUB EmptySet A.
Proof ieieep2_Out.
Proof Build_EQ A EmptySet step1 step2.
End its_empty_implies_equals_emptyset_proof.

Theorem its_empty_implies_equals_emptyset :
forall (A : Ens) (k : Its_empty A), EQ A EmptySet.