theorem
  for x2 being Element of M2
  holds [2,x2] in FreeAtoms(<*M1,M2*>) & [2,x2] in FreeAtoms(<*M1,M2,M3*>)
proof
  let x2 be Element of M2;
  2 in {2} & x2 in the carrier of M2 by TARSKI:def 1;
  then [2,x2] in [: {2}, the carrier of M2 :] by ZFMISC_1:def 2;
  then A1: [2,x2] in [: {1}, the carrier of M1 :]\/[: {2}, the carrier of M2 :]
    by XBOOLE_0:def 3;
  then [2,x2] in ([: {1}, the carrier of M1 :] \/ [: {2}, the carrier of M2 :])
    \/ [: {3}, the carrier of M3 :] by XBOOLE_0:def 3;
  hence thesis by A1, Th13, Th14;
end;
