reserve x,O for set,
  o for Element of O,
  G,H,I for GroupWithOperators of O,
  A, B for Subset of G,
  N for normal StableSubgroup of G,
  H1,H2,H3 for StableSubgroup of G,
  g1,g2 for Element of G,
  h1,h2 for Element of H1,
  h for Homomorphism of G,H;

theorem Th49:
  rng h = the carrier of Image h
proof
  the carrier of Image h = h .: (the carrier of G) by Def22
    .= h .: (dom h) by FUNCT_2:def 1
    .= rng h by RELAT_1:113;
  hence thesis;
end;
