Consider the following premises. r_6 -> w. r -> t. r <-> w. t -> r_6. Can we infer ~(r_6 <-> r) from them?
 From r <-> w we can infer w -> r. From r -> t, t -> r_6 we can infer r -> r_6. From r_6 -> w, w -> r we can infer r_6 -> r. Finally, from r_6 -> r, r -> r_6 we can infer r_6 <-> r, which contradicts ~(r_6 <-> r). Therefore, the answer is no.