theorem
  for R being transitive Tolerance of X holds y in Class(R,x) & z in
  Class(R,x) implies [y,z] in R
proof
  let R be transitive Tolerance of X;
  assume that
A1: y in Class(R,x) and
A2: z in Class(R,x);
  [z,x] in R by A2,Th19;
  then
A3: [x,z] in R by Th6;
  [y,x] in R by A1,Th19;
  hence thesis by A3,Th7;
end;
