Consider the following premises. p <-> q_2. ~q_2. p_2 -> p. p -> p_2. Can we infer p_2 from them? If possible, name the inference rules being used at each step.
 From p_2 -> p, p -> p_2 we can infer p_2 <-> p via biconditional introduction. From p <-> q_2, ~q_2 we can infer ~p via biconditional elimination. Finally, from p_2 <-> p, ~p we can infer ~p_2 via biconditional elimination, which contradicts p_2. Therefore, the answer is no.