Consider the following premises. t_1 -> r_1. ~t_1. t_1 <-> r_1. Can we infer ~r_1 from them? If possible, name the inference rules being used at each step.
 From t_1 <-> r_1 we can infer r_1 -> t_1 via biconditional elimination. From t_1 -> r_1, r_1 -> t_1 we can infer t_1 <-> r_1 via biconditional introduction. Finally, from t_1 <-> r_1, ~t_1 we can infer ~r_1 via biconditional elimination. Therefore, the answer is yes.