reserve a,b,p,x,x9,x1,x19,x2,y,y9,y1,y19,y2,z,z9,z1,z2 for object,
   X,X9,Y,Y9,Z,Z9 for set;
reserve A,D,D9 for non empty set;
reserve f,g,h for Function;

theorem Th23:
  (f +* g)|(dom g) = g
proof
  dom f \/ dom g = dom(f +* g) by Def1;
  then
A1: dom((f +* g)|(dom g)) = dom g by RELAT_1:62,XBOOLE_1:7;
  for x being object st x in dom g holds ((f +* g)|(dom g)).x = g.x
  proof
    let x be object;
    x in dom g implies (f +* g).x = g.x by Th13;
    hence thesis by A1,FUNCT_1:47;
  end;
  hence thesis by A1;
end;
