reserve x,y for set,
  k,n for Nat,
  i for Integer,
  G for Group,
  a,b,c ,d,e for Element of G,
  A,B,C,D for Subset of G,
  H,H1,H2,H3,H4 for Subgroup of G ,
  N1,N2 for normal Subgroup of G,
  F,F1,F2 for FinSequence of the carrier of G,
  I,I1,I2 for FinSequence of INT;

theorem Th53:
  1_G in commutators(H1,H2)
proof
A1: 1_G in H2 by GROUP_2:46;
  [.1_G,1_G.] = 1_G & 1_G in H1 by Th19,GROUP_2:46;
  hence thesis by A1,Th52;
end;
