Consider the following premises. p -> q_10. ~q_10 -> q. q_10 -> p. ~p. Can we infer ~q from them? If possible, name the inference rules being used at each step.
 From p -> q_10, q_10 -> p we can infer p <-> q_10 via biconditional introduction. From p <-> q_10, ~p we can infer ~q_10 via biconditional elimination. Finally, from ~q_10 -> q, ~q_10 we can infer q via modus ponens, which contradicts ~q. Therefore, the answer is no.