Consider the following premises. forall x_7: Q_7(x_7) -> R_7(x_7). forall x_7: P_7(x_7) or Q_7(x_7). forall x_7: P_7(x_7) -> R_7(x_7). forall x_7: P_3(x_7). Can we infer R_7(a_2) from them? If possible, name the inference rules being used at each step.
 From forall x_7: P_7(x_7) -> R_7(x_7), forall x_7: Q_7(x_7) -> R_7(x_7), forall x_7: P_7(x_7) or Q_7(x_7) we can infer forall x_7: R_7(x_7) via universal disjunction elimination. From forall x_7: P_3(x_7), forall x_7: R_7(x_7) we can infer forall x_7: P_3(x_7) and R_7(x_7) via universal conjunction. From forall x_7: P_3(x_7) and R_7(x_7) we can infer P_3(a_2) and R_7(a_2) via universal instantiation. Finally, from P_3(a_2) and R_7(a_2) we can infer R_7(a_2) via simplification. Therefore, the answer is yes.