Exact conditions for the symmetry of a loop

It is well known that a loop looks the same from both ends provided that its topology is approximately symmetrical with respect to the midpoint of the line. However, to the best of the author´s knowledge, no explicit proof has ever been given to confirm or refute this property. In this article, it is mathematically proved for the first time that a telephone line, regardless of its topology, is always a symmetric channel (same frequency transfer function from either side) provided that the source and load impedances be the same.