theorem Th107:
  R.:dom R = rng R
proof
  thus R.:dom R c= rng R by Th105;
  let y be object;
  assume y in rng R;
  then consider x being object such that
A1: [x,y] in R by XTUPLE_0:def 13;
  x in dom R by A1,XTUPLE_0:def 12;
  hence thesis by A1,Def11;
end;
