Consider the following premises. t -> t_1. t_1 -> t_3. t_3 -> w. w -> t. Can we infer ~(t_3 <-> w) from them?
 From w -> t, t -> t_1 we can infer w -> t_1. From w -> t_1, t_1 -> t_3 we can infer w -> t_3. Finally, from t_3 -> w, w -> t_3 we can infer t_3 <-> w, which contradicts ~(t_3 <-> w). Therefore, the answer is no.