Consider the following premises. forall x_16: P_16(x_16). forall x_16: P_16(x_16) <-> U(x_16). Can we infer U(a_9) or w from them? If possible, name the inference rules being used at each step.
 From forall x_16: P_16(x_16) <-> U(x_16) we can infer forall x_16: P_16(x_16) -> U(x_16) via universal biconditional elimination. From forall x_16: P_16(x_16) -> U(x_16), forall x_16: P_16(x_16) we can infer forall x_16: U(x_16) via universal modus ponens. From forall x_16: U(x_16) we can infer U(a_9) via universal instantiation. Finally, from U(a_9) we can infer U(a_9) or w via addition. Therefore, the answer is yes.