reserve A,X,X1,X2,Y,Y1,Y2 for set, a,b,c,d,x,y,z for object;
reserve P,P1,P2,Q,R,S for Relation;

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;
