reserve X for set;
reserve UN for Universe;

theorem Th35:
  for x being Element of UN
  for y,z being object st x = [y,z] holds y is Element of UN &
  z is Element of UN
  proof
    let x be Element of UN;
    let y,z be object;
    assume
A1: x = [y,z];
A2: UN is axiom_GU1;
    {y} in x in UN by A1,TARSKI:def 2;
    then y in {y} in UN by A2,TARSKI:def 1;
    hence y is Element of UN by A2;
    {y,z} in x in UN by A1,TARSKI:def 2;
    then z in {y,z} in UN by A2,TARSKI:def 2;
    hence z is Element of UN by A2;
  end;
