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

theorem Th107:
  Maps U c= U
  proof
    let o be object;
    assume o in Maps U;
    then consider A,B be Element of U,f be Element of Funcs U such that
A1: o = [[A,B],f] and
    B = {} implies A = {} and
A2: f is Function of A,B;
    f in bool [:A,B:] by A2;
    then f in U by CLASSES4:13;
    hence o in U by A1,CLASSES2:58;
  end;
