
theorem Th5:
  for T being non empty TopSpace, p,q being Point of T holds (
  T_0-canonical_map(T)).q = (T_0-canonical_map(T)).p iff [q,p] in
  Indiscernibility(T)
proof
  let T be non empty TopSpace;
  let p,q be Point of T;
  set F = T_0-canonical_map(T);
  set R = Indiscernibility(T);
  hereby
    assume F.q = F.p;
    then q in F.p by BORSUK_1:28;
    then q in Class(R,p) by Th4;
    hence [q,p] in R by EQREL_1:19;
  end;
  assume [q,p] in R;
  then Class(R,q) = Class(R,p) by EQREL_1:35;
  then F.q = Class(R,p) by Th4;
  hence thesis by Th4;
end;
