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 Th39:
  A c= M & B c= M implies {A,B} is MSSubsetFamily of M
proof
  assume A c= M & B c= M;
  then {A} is MSSubsetFamily of M & {B} is MSSubsetFamily of M by Th38;
  then {A} (\/) {B} is MSSubsetFamily of M by Th34;
  hence thesis by PZFMISC1:10;
end;
