 reserve x,y,X,Y for set;
reserve G for non empty multMagma,
  D for set,
  a,b,c,r,l for Element of G;
reserve M for non empty multLoopStr;
reserve H for non empty SubStr of G,
  N for non empty MonoidalSubStr of G;

theorem Th70:
  for F being non empty SubStr of GPFuncs X
  for f,g being Element of F holds f [*] g = g (*) f
proof
  let F be non empty SubStr of GPFuncs X;
  let f,g be Element of F;
  carr(F) c= carr(GPFuncs X) by Th23;
  then reconsider f9 = f, g9 = g as Element of GPFuncs X;
  f[*]g = f9[*]g9 by Th25;
  hence thesis by Def37;
end;
