Consider the following premises. q_1 -> t. forall x_15: P_15(x_15) -> Q_15(x_15). Q_15(a_10) -> q_1. forall x_15: Q_15(x_15) -> P_15(x_15). Can we infer P_15(a_10) -> t from them? If possible, name the inference rules being used at each step.
 From forall x_15: P_15(x_15) -> Q_15(x_15), forall x_15: Q_15(x_15) -> P_15(x_15) we can infer forall x_15: P_15(x_15) <-> Q_15(x_15) via universal biconditional introduction. From forall x_15: P_15(x_15) <-> Q_15(x_15) we can infer forall x_15: P_15(x_15) -> Q_15(x_15) via universal biconditional elimination. From forall x_15: P_15(x_15) -> Q_15(x_15) we can infer P_15(a_10) -> Q_15(a_10) via universal instantiation. From Q_15(a_10) -> q_1, q_1 -> t we can infer Q_15(a_10) -> t via transitivity. Finally, from P_15(a_10) -> Q_15(a_10), Q_15(a_10) -> t we can infer P_15(a_10) -> t via transitivity. Therefore, the answer is yes.