reserve x,y,X,Y for set,
  k,l,n for Nat,
  i,i1,i2,i3,j for Integer,
  G for Group,
  a,b,c,d for Element of G,
  A,B,C for Subset of G,
  H,H1,H2, H3 for Subgroup of G,
  h for Element of H,
  F,F1,F2 for FinSequence of the carrier of G,
  I,I1,I2 for FinSequence of INT;

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;
