Consider the following premises. r_2 <-> t. w or ~t. Can we infer ~(r_2 -> w) from them?
 From w or ~t we can infer t -> w. From r_2 <-> t we can infer r_2 -> t. Finally, from r_2 -> t, t -> w we can infer r_2 -> w, which contradicts ~(r_2 -> w). Therefore, the answer is no.