Consider the following premises. exists x: P(x) <-> U_3(x). forall x: U_3(x) <-> W(x). Can we infer exists x: W(x) -> P(x) from them? If possible, name the inference rules being used at each step.
 From forall x: U_3(x) <-> W(x) we can infer forall x: W(x) -> U_3(x) via universal biconditional elimination. From exists x: P(x) <-> U_3(x) we can infer exists x: U_3(x) -> P(x) via existential biconditional elimination. Finally, from forall x: W(x) -> U_3(x), exists x: U_3(x) -> P(x) we can infer exists x: W(x) -> P(x) via existential transitivity. Therefore, the answer is yes.