theorem Th85:
  for X being non empty set, PX being a_partition of X
  for Pi being set st Pi in PX ex x being Element of X st x in Pi
proof
  let X be non empty set, PX be a_partition of X;
  let Pi be set;
  assume Pi in PX;
  then reconsider Pi as Element of PX;
  set q = the Element of Pi;
  reconsider q as Element of X;
  take q;
  thus thesis;
end;
