reserve U for Universe;
reserve x for Element of U;
reserve U1,U2 for Universe;

theorem Th103:
  Funcs U c< U
  proof
    thus Funcs U c= U
    proof
      set FAB = {Funcs (A,B) where A, B is Element of U : not contradiction};
      now
        let o be object;
        assume o in the set of all Funcs(A,B) where A,B is Element of U;
        then consider A,B be Element of U such that
A1:     o = Funcs(A,B);
        thus o in U by A1;
      end;
      then the set of all Funcs(A,B) where A,B is Element of U c= U;
      then union the set of all Funcs(A,B) where A,B is Element of U
        c= union U by ZFMISC_1:77;
      hence Funcs U c= U by CLASSES4:81;
    end;
    {{}} is Element of U by CLASSES2:56,57;
    hence thesis by Th2;
  end;
