Consider the following premises. t_1 -> t_3. w -> t. t_3 -> w. t -> t_1. Can we infer ~(t_3 <-> w) from them? If possible, name the inference rules being used at each step.
 From w -> t, t -> t_1 we can infer w -> t_1 via transitivity. From w -> t_1, t_1 -> t_3 we can infer w -> t_3 via transitivity. Finally, from t_3 -> w, w -> t_3 we can infer t_3 <-> w via biconditional introduction, which contradicts ~(t_3 <-> w). Therefore, the answer is no.