reserve T for non empty TopSpace,
  A, B for Subset of T,
  F, G for Subset-Family of T;
reserve x for Point of T;

theorem Th48:
  x is_a_condensation_point_of A & A c= B implies x
  is_a_condensation_point_of B
proof
  assume that
A1: x is_a_condensation_point_of A and
A2: A c= B;
  for N being a_neighborhood of x holds N /\ B is not countable
  proof
    let N be a_neighborhood of x;
    N /\ A c= N /\ B by A2,XBOOLE_1:26;
    hence thesis by A1;
  end;
  hence thesis;
end;
