reserve e for set;
reserve C,C1,C2,C3 for AltCatStr;
reserve C for non empty AltCatStr,
  o for Object of C;
reserve C for non empty transitive AltCatStr;

theorem Th26:
  for D1,D2 being non empty transitive SubCatStr of C st the
  carrier of D1 = the carrier of D2 & the Arrows of D1 = the Arrows of D2 holds
  the AltCatStr of D1 = the AltCatStr of D2
proof
  let D1,D2 be non empty transitive SubCatStr of C;
  assume
  the carrier of D1 = the carrier of D2 & the Arrows of D1 = the Arrows of D2;
  then D1 is SubCatStr of D2 & D2 is SubCatStr of D1 by Th24;
  hence thesis by Th22;
end;
