theorem Th25:
  for x st x in X holds Class(id X,x) = {x}
proof
  let x;
A1: now
    let y;
    assume y in Class(id X,x);
    then [y,x] in id X by Th19;
    hence y = x by RELAT_1:def 10;
  end;
  assume x in X;
  then for y being object holds y in Class(id X,x) iff y = x by A1,Th20;
  hence thesis by TARSKI:def 1;
end;
