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 x1 being Element of M1 holds [1,x1] in FreeAtoms(<*M1*>) &
     [1,x1] in FreeAtoms(<*M1,M2*>) & [1,x1] in FreeAtoms(<*M1,M2,M3*>)
proof
  let x1 be Element of M1;
  1 in {1} & x1 in the carrier of M1 by TARSKI:def 1;
  then A1: [1,x1] in [: {1}, the carrier of M1 :] by ZFMISC_1:def 2;
  then A2: [1,x1] in [: {1}, the carrier of M1 :]\/[: {2}, the carrier of M2 :]
    by XBOOLE_0:def 3;
  then [1,x1] 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, A2, Th12, Th13, Th14;
end;
