  We give a short and elementary proof of a $(q, \mu, \nu)$-deformed Binomial
distribution identity arising in the study of the $(q, \mu, \nu)$-Boson process
and the $(q, \mu, \nu)$-TASEP. This identity found by Corwin in [4] was a key
technical step to prove an intertwining relation between the Markov transition
matrices of these two classes of discrete-time Markov chains. This was used in
turn to derive exact formulas for a large class of observables of both these
processes.
