A probability density function theorem for the modulo y values of the sum of two statistically independent processes

It is demonstrated that when any process α(t) (random or deterministic) is added to a random process φ(t), where φ(t), modulo y, is uniformly distributed and statistically independent of α(t), the resultant random process, modulo y, is also uniformly distributed. The process α(t) need not be independent of φ(t).