reserve P,Q,X,Y,Z for set, p,x,x9,x1,x2,y,z for object;

theorem
  for f being Relation of X,Y holds (id X)*f = f & f*(id Y) = f
proof
  let f be Relation of X,Y;
  dom f c= X;
  hence (id X)*f = f by RELAT_1:51;
  rng f c= Y;
  hence thesis by RELAT_1:53;
end;
