reserve A,X,X1,X2,Y,Y1,Y2 for set, a,b,c,d,x,y,z for object;
reserve P,P1,P2,Q,R,S for Relation;

theorem
  (for x st x in X holds [x,x] in R) implies id X c= R
proof
  assume
A1: for x st x in X holds [x,x] in R;
  let x,y;
  assume [x,y] in id X;
  then x in X & x=y by Def8;
  hence thesis by A1;
end;
