Consider the following premises. ~q_1. q_10 -> r_3. q_1 <-> q_10. r_3 -> q_1. Can we infer ~r_3 from them? If possible, name the inference rules being used at each step.
 From q_1 <-> q_10 we can infer q_1 -> q_10 via biconditional elimination. From q_1 -> q_10, q_10 -> r_3 we can infer q_1 -> r_3 via transitivity. From r_3 -> q_1, q_1 -> r_3 we can infer r_3 <-> q_1 via biconditional introduction. Finally, from r_3 <-> q_1, ~q_1 we can infer ~r_3 via biconditional elimination. Therefore, the answer is yes.