reserve X,Y,Z for set, x,y,z for object;
reserve i,j for Nat;
reserve A,B,C for Subset of X;
reserve R,R1,R2 for Relation of X;
reserve AX for Subset of [:X,X:];
reserve SFXX for Subset-Family of [:X,X:];
reserve EqR,EqR1,EqR2,EqR3 for Equivalence_Relation of X;

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;
