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;
reserve e,u for object,
  A for Subset of X;

theorem
  (id X).:A = A
proof
  now
    let e be object;
    thus e in A implies
     ex u being object st u in dom id X & u in A & e = (id X).u
    proof
      assume
A1:   e in A;
      take e;
      thus e in dom id X by A1;
      thus e in A by A1;
      thus thesis by A1,Th17;
    end;
    assume ex u being object st u in dom id X & u in A & e = (id X).u;
    hence e in A by Th17;
  end;
  hence thesis by Def6;
end;
