Consider the following premises. ~P_9(h). forall x_9: P_9(x_9) <-> P_1(x_9). Can we infer P_1(h) from them? If possible, name the inference rules being used at each step.
 From forall x_9: P_9(x_9) <-> P_1(x_9) we can infer forall x_9: P_1(x_9) -> P_9(x_9) via universal biconditional elimination. From forall x_9: P_1(x_9) -> P_9(x_9) we can infer P_1(h) -> P_9(h) via universal instantiation. Finally, from P_1(h) -> P_9(h), ~P_9(h) we can infer ~P_1(h) via modus tollens, which contradicts P_1(h). Therefore, the answer is no.