Consider the following premises. forall x_11: Q_11(x_11) -> R_11(x_11). forall x_11: P_11(x_11) -> Q_11(x_11). p -> P_11(a_10). R_11(a_10) -> p. Can we infer P_11(a_10) <-> R_11(a_10) from them? If possible, name the inference rules being used at each step.
 From forall x_11: P_11(x_11) -> Q_11(x_11), forall x_11: Q_11(x_11) -> R_11(x_11) we can infer forall x_11: P_11(x_11) -> R_11(x_11) via universal transitivity. From forall x_11: P_11(x_11) -> R_11(x_11) we can infer P_11(a_10) -> R_11(a_10) via universal instantiation. From R_11(a_10) -> p, p -> P_11(a_10) we can infer R_11(a_10) -> P_11(a_10) via transitivity. Finally, from P_11(a_10) -> R_11(a_10), R_11(a_10) -> P_11(a_10) we can infer P_11(a_10) <-> R_11(a_10) via biconditional introduction. Therefore, the answer is yes.