Consider the following premises. exists x_9: Q_2(x_9). forall x_9: T_2(x_9) -> T_1(x_9). forall x_9: T_1(x_9) -> T_2(x_9). forall x_9: T_1(x_9). Can we infer exists x_9: Q_2(x_9) and T_2(x_9) from them? If possible, name the inference rules being used at each step.
 From forall x_9: T_1(x_9) -> T_2(x_9), forall x_9: T_2(x_9) -> T_1(x_9) we can infer forall x_9: T_1(x_9) <-> T_2(x_9) via universal biconditional introduction. From forall x_9: T_1(x_9) <-> T_2(x_9) we can infer forall x_9: T_1(x_9) -> T_2(x_9) via universal biconditional elimination. From forall x_9: T_1(x_9) -> T_2(x_9), forall x_9: T_1(x_9) we can infer forall x_9: T_2(x_9) via universal modus ponens. Finally, from exists x_9: Q_2(x_9), forall x_9: T_2(x_9) we can infer exists x_9: Q_2(x_9) and T_2(x_9) via existential conjunction. Therefore, the answer is yes.