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