Consider the following premises. forall x_8: Q_8(x_8) -> P(x_8). P(i_1). forall x_8: P(x_8) -> Q_8(x_8). Can we infer Q_8(i_1) from them? If possible, name the inference rules being used at each step.
 From forall x_8: P(x_8) -> Q_8(x_8), forall x_8: Q_8(x_8) -> P(x_8) we can infer forall x_8: P(x_8) <-> Q_8(x_8) via universal biconditional introduction. From forall x_8: P(x_8) <-> Q_8(x_8) we can infer P(i_1) <-> Q_8(i_1) via universal instantiation. From P(i_1) <-> Q_8(i_1) we can infer P(i_1) -> Q_8(i_1) via biconditional elimination. Finally, from P(i_1) -> Q_8(i_1), P(i_1) we can infer Q_8(i_1) via modus ponens. Therefore, the answer is yes.