reserve
  I for set,
  E for non empty set;
reserve A for ObjectsFamily of I,EnsCat E;

theorem
  (for I,A holds product A in E) implies EnsCat E is with_products
  proof
    assume
A1: for I,A holds product A in E;
    let I,A;
    take EnsCatProductObj A, EnsCatProduct A;
    product A in E by A1;
    hence thesis by Th8;
  end;
