Consider the following premises. p_13 <-> r_3. r_3 -> p_13. s_3 -> p_13. p_13 -> s_3. ~s_3. Can we infer r_3 from them? If possible, name the inference rules being used at each step.
 From p_13 -> s_3, s_3 -> p_13 we can infer p_13 <-> s_3 via biconditional introduction. From p_13 <-> r_3 we can infer p_13 -> r_3 via biconditional elimination. From p_13 -> r_3, r_3 -> p_13 we can infer p_13 <-> r_3 via biconditional introduction. From p_13 <-> s_3, ~s_3 we can infer ~p_13 via biconditional elimination. Finally, from p_13 <-> r_3, ~p_13 we can infer ~r_3 via biconditional elimination, which contradicts r_3. Therefore, the answer is no.