Consider the following premises. forall y: W(y) <-> U_4(y). forall y: U_4(y) <-> P(y). forall y: W(y) or P(y). Can we infer forall y: U_4(y) from them? If possible, name the inference rules being used at each step.
 From forall y: U_4(y) <-> P(y) we can infer forall y: P(y) -> U_4(y) via universal biconditional elimination. From forall y: W(y) <-> U_4(y) we can infer forall y: W(y) -> U_4(y) via universal biconditional elimination. Finally, from forall y: W(y) -> U_4(y), forall y: P(y) -> U_4(y), forall y: W(y) or P(y) we can infer forall y: U_4(y) via universal disjunction elimination. Therefore, the answer is yes.