theorem
  for G being Group, a being Element of G holds (for H being strict
  Subgroup of G holds H is not maximal) implies a in Phi(G)
proof
  let G be Group, a be Element of G;
  assume for H being strict Subgroup of G holds H is not maximal;
  then Phi(G) = the multMagma of G by Def7;
  hence thesis by STRUCT_0:def 5;
end;
