 reserve x,y,z,t for object,X,Y,Z,W for set;
 reserve R,S,T for Relation;

theorem Th26:
  dom CL R = rng CL R
proof
  thus dom CL R c= rng CL R
  proof
    let x be object;
    assume x in dom CL R;
    then consider y being object such that
A1: [x,y] in CL R by XTUPLE_0:def 12;
    [x,y] in id dom R by A1,XBOOLE_0:def 4;
    then [x,x] in CL R by A1,RELAT_1:def 10;
    hence thesis by XTUPLE_0:def 13;
  end;
  let x be object;
  assume x in rng CL R;
  then consider y being object such that
A2: [y,x] in CL R by XTUPLE_0:def 13;
  [y,x] in id dom R by A2,XBOOLE_0:def 4;
  then [x,x] in CL R by A2,RELAT_1:def 10;
  hence thesis by XTUPLE_0:def 12;
end;
