reserve X,Y,Z,x,y,z for set;
reserve T,R for Tolerance of X;

theorem
  for T being Tolerance of X st {} is TolClass of T holds T={}
proof
  let T be Tolerance of X;
  assume {} is TolClass of T;
  then reconsider O0 = {} as TolClass of T;
  assume T <> {};
  then consider x,y being object such that
A1: [x,y] in T;
  x in X by A1,ZFMISC_1:87;
  then ex z st z in O0 & not [x,z] in T by Def2;
  hence contradiction;
end;
