reserve X,X1,X2,Y,Y1,Y2 for set, p,x,x1,x2,y,y1,y2,z,z1,z2 for object;
reserve f,g,g1,g2,h for Function,
  R,S for Relation;

theorem
  (id X)" = id X
proof
  dom id X = X;
  then
A1: (id X)"*(id X) = id X by Th38;
  dom((id X)") = rng id X & rng id X = X by Th32;
  hence thesis by A1,Th23;
end;
