Consider the following premises. q <-> p. p_11 -> p. p -> p_11. ~q. Can we infer p_11 from them? If possible, name the inference rules being used at each step.
 From p_11 -> p, p -> p_11 we can infer p_11 <-> p via biconditional introduction. From q <-> p, ~q we can infer ~p via biconditional elimination. From p_11 <-> p we can infer p_11 -> p via biconditional elimination. Finally, from p_11 -> p, ~p we can infer ~p_11 via modus tollens, which contradicts p_11. Therefore, the answer is no.