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

theorem Th28:
  CL R = id dom CL R
proof
  let x,y be object;
  thus [x,y] in CL R implies [x,y] in id dom CL R
  proof
    assume
A1: [x,y] in CL R;
    then [x,y] in id dom R by XBOOLE_0:def 4; then
A2: x = y by RELAT_1:def 10;
    x in dom CL R by A1,XTUPLE_0:def 12;
    hence thesis by A2,RELAT_1:def 10;
  end;
  assume
A3: [x,y] in id dom CL R;
  then x in dom CL R by RELAT_1:def 10; then
A4: ex z being object st [x,z] in CL R by XTUPLE_0:def 12;
  x = y by A3,RELAT_1:def 10;
  hence thesis by A4,Th25;
end;
