reserve I, G, H for set, i, x for object,
  A, B, M for ManySortedSet of I,
  sf, sg, sh for Subset-Family of I,
  v, w for Subset of I,
  F for ManySortedFunction of I;
reserve X, Y, Z for ManySortedSet of I;
reserve SF, SG, SH for MSSubsetFamily of M,
  SFe for non-empty MSSubsetFamily of M,
  V, W for ManySortedSubset of M;

theorem Th33:
  A in SF implies A is ManySortedSubset of M
proof
A1: SF c= bool M by PBOOLE:def 18;
  assume A in SF;
  then A in bool M by A1,PBOOLE:9;
  then A c= M by MBOOLEAN:18;
  hence thesis by PBOOLE:def 18;
end;
