
theorem Th1:
  for X being set st Total X c= id X holds X is trivial
proof
  let X be set;
  assume
A1: Total X c= id X;
  assume X is non trivial;
  then consider x, y being object such that
A2: x in X & y in X and
A3: x <> y by ZFMISC_1:def 10;
  [x,y] in Total X by A2,TOLER_1:2;
  hence thesis by A1,A3,RELAT_1:def 10;
end;
