theorem Th25:
  for x,y being object holds [x,y] in CL R implies x in dom CL R & x = y
proof let x,y be object;
  assume
A1: [x,y] in CL R;
  then [x,y] in id dom R by XBOOLE_0:def 4;
  hence thesis by A1,RELAT_1:def 10,XTUPLE_0:def 12;
end;
