reserve X for set;
reserve UN for Universe;

theorem Th36:
  for X being Element of UN holds proj1 X is Element of UN &
  proj2 X is Element of UN
  proof
    let X be Element of UN;
    proj1 X in bool union union X &
      proj2 X in bool union union X &
      UN is axiom_GU1 by Th1;
    hence thesis;
  end;
