reserve x,y,z, X,Y,Z for set,
  n for Element of NAT;
reserve A for set,
  D for non empty set,
  a,b,c,l,r for Element of D,
  o,o9 for BinOp of D,
  f,g,h for Function of A,D;
reserve G for non empty multMagma;

theorem Th22:
  for G being unital non empty multMagma holds 1..:(G,X) = X -->
  the_unity_wrt the multF of G
proof
  let G be unital non empty multMagma;
  .:(G,X) = multLoopStr(#Funcs(X, carr(G)), (op(G), carr(G)).:X, (X -->
    the_unity_wrt op(G))#) by Def3;
  hence thesis;
end;
