reserve X for set;
reserve UN for Universe;

theorem
  for R being Relation st dom R is Element of UN &
  rng R is Element of UN holds R is Element of UN
  proof
    let R be Relation;
    assume that
A1: dom R is Element of UN and
A2: rng R is Element of UN;
A3: R c= [: dom R, rng R :] by RELAT_1:7;
    [: dom R, rng R:] is Element of UN by A1,A2,CLASSES2:61;
    hence thesis by A3,Th13;
  end;
