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.