Consider the following premises. q_2 or ~p_4. ~p_4 -> p_22. ~q_2. p_22 <-> q_22. Can we infer q_22 from them? If possible, name the inference rules being used at each step.
 From p_22 <-> q_22 we can infer p_22 -> q_22 via biconditional elimination. From q_2 or ~p_4 we can infer p_4 -> q_2 via rewriting. From p_4 -> q_2, ~q_2 we can infer ~p_4 via modus tollens. From ~p_4 -> p_22, p_22 -> q_22 we can infer ~p_4 -> q_22 via transitivity. Finally, from ~p_4 -> q_22, ~p_4 we can infer q_22 via modus ponens. Therefore, the answer is yes.