Consider the following premises. forall x_12: Q_12(x_12) -> R_6(x_12). forall x_12: P_12(x_12) <-> Q_12(x_12). R_6(a_5) -> r. Can we infer P_12(a_5) -> r from them? If possible, name the inference rules being used at each step.
 From forall x_12: P_12(x_12) <-> Q_12(x_12) we can infer forall x_12: P_12(x_12) -> Q_12(x_12) via universal biconditional elimination. From forall x_12: P_12(x_12) -> Q_12(x_12), forall x_12: Q_12(x_12) -> R_6(x_12) we can infer forall x_12: P_12(x_12) -> R_6(x_12) via universal transitivity. From forall x_12: P_12(x_12) -> R_6(x_12) we can infer P_12(a_5) -> R_6(a_5) via universal instantiation. Finally, from P_12(a_5) -> R_6(a_5), R_6(a_5) -> r we can infer P_12(a_5) -> r via transitivity. Therefore, the answer is yes.