
theorem Th3:
  for T being non empty TopSpace, C being set holds C is Point of
  T_0-reflex(T) iff ex p being Point of T st C = Class(Indiscernibility(T),p)
proof
  let T be non empty TopSpace;
  set TR = T_0-reflex(T);
  set R = Indiscernibility(T);
  let C be set;
  hereby
    assume C is Point of TR;
    then C in the carrier of TR;
    then C in Indiscernible(T) by BORSUK_1:def 7;
    hence ex p being Point of T st C = Class(R,p) by EQREL_1:36;
  end;
  assume ex p being Point of T st C = Class(R,p);
  then C in Class R by EQREL_1:def 3;
  hence thesis by BORSUK_1:def 7;
end;
