theorem Th175:
  for R being X-defined Y-valued Relation holds R c= [:X,Y:]
  proof
    let R be X-defined Y-valued Relation;
A1:  R c= [:dom R,rng R:] by Th1;
    dom R c= X & rng R c= Y by Def16,Def17;
    then [:dom R,rng R:] c= [:X,Y:] by ZFMISC_1:96;
    hence thesis by A1;
  end;
