reserve x,y,z,X for set,
  T for Universe;

theorem Th7:
  for R being RelStr, S being SubRelStr of R, T being SubRelStr of
  S holds T is SubRelStr of R
proof
  let R be RelStr, S be SubRelStr of R, T be SubRelStr of S;
  the InternalRel of S c= the InternalRel of R & the InternalRel of T c=
  the InternalRel of S by YELLOW_0:def 13;
  then
A1: the InternalRel of T c= the InternalRel of R;
  the carrier of S c= the carrier of R & the carrier of T c= the carrier
  of S by YELLOW_0:def 13;
  then the carrier of T c= the carrier of R;
  hence thesis by A1,YELLOW_0:def 13;
end;
