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 Th126:
  R"rng R = dom R
proof
  thus R"rng R c= dom R by Th124;
  let x be object;
  assume x in dom R;
  then consider y being object such that
A1: [x,y] in R by XTUPLE_0:def 12;
  y in rng R by A1,XTUPLE_0:def 13;
  hence thesis by A1,Def12;
end;
