theorem Th49:
  h is Homomorphism of G,Image h
proof
  rng h = the carrier of Image h & dom h = the carrier of G by Th44,
FUNCT_2:def 1;
  then reconsider f9 = h as Function of G, Image h by RELSET_1:4;
  now
    let a,b;
    thus f9.a * f9.b = h.a * h.b by GROUP_2:43
      .= f9.(a * b) by Def6;
  end;
  hence thesis by Def6;
end;
