Consider the following premises. p_3 <-> p_6. p_6 -> q_1. ~q_1. Can we infer p_3 from them? If possible, name the inference rules being used at each step.
 From p_6 -> q_1, ~q_1 we can infer ~p_6 via modus tollens. From p_3 <-> p_6 we can infer p_3 -> p_6 via biconditional elimination. Finally, from p_3 -> p_6, ~p_6 we can infer ~p_3 via modus tollens, which contradicts p_3. Therefore, the answer is no.