 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
  for F being unital non empty SubStr of D*+^ holds
  the_unity_wrt the multF of F = {}
proof
  let F be unital non empty SubStr of D*+^;
  set p = the_unity_wrt op(F);
  reconsider q = p as Element of F qua SubStr of D*+^;
  q^{} = p by FINSEQ_1:34
    .= p[*]p by SETWISEO:15
    .= q^q by Th63;
  hence thesis by FINSEQ_1:33;
end;
