Consider the following premises. p_3 -> q. q -> p_3. q. Can we infer ~p_3 from them?
 From p_3 -> q, q -> p_3 we can infer p_3 <-> q. From p_3 <-> q we can infer q -> p_3. Finally, from q -> p_3, q we can infer p_3, which contradicts ~p_3. Therefore, the answer is no.