reserve x,y,z for object, X for set, I for non empty set, i,j for Element of I,
    M0 for multMagma-yielding Function,
    M for non empty multMagma-yielding Function,
    M1, M2, M3 for non empty multMagma,
    G for Group-like multMagma-Family of I,
    H for Group-like associative multMagma-Family of I;

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;
