reserve A,B,X,X1,Y,Y1,Y2,Z for set, a,x,y,z for object;
reserve P,R for Relation of X,Y;

theorem Th13:
  id X c= [:X,X:]
proof
  [:X,X:] c= [:X,X:];
  then reconsider R = [:X,X:] as Relation of X,X;
  for x,y being object holds [x,y] in id X implies [x,y] in R
  proof let x,y be object;
    assume [x,y] in id X;
    then x in X & x = y by RELAT_1:def 10;
    hence thesis by ZFMISC_1:87;
  end;
  hence thesis;
end;
