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 Th53:
  for N1,N2 being strict normal Subgroup of G holds the carrier of
  N1 "\/" N2 = N1 * N2
proof
  let N1,N2 be strict normal Subgroup of G;
  N1 * N2 = N2 * N1 by GROUP_3:125;
  hence thesis by Th51;
end;
