Consider the following premises. p_4 <-> q_3. ~q_3. q_3 -> p_4. Can we infer p_4 from them? If possible, name the inference rules being used at each step.
 From p_4 <-> q_3 we can infer p_4 -> q_3 via biconditional elimination. From p_4 -> q_3, q_3 -> p_4 we can infer p_4 <-> q_3 via biconditional introduction. Finally, from p_4 <-> q_3, ~q_3 we can infer ~p_4 via biconditional elimination, which contradicts p_4. Therefore, the answer is no.