Consider the following premises. w. R(c) or u. forall z: U_1(z) -> R(z). forall z: R(z) -> U_1(z). u -> U_1(c). Can we infer w and U_1(c) from them? If possible, name the inference rules being used at each step.
 From forall z: R(z) -> U_1(z), forall z: U_1(z) -> R(z) we can infer forall z: R(z) <-> U_1(z) via universal biconditional introduction. From forall z: R(z) <-> U_1(z) we can infer R(c) <-> U_1(c) via universal instantiation. From R(c) <-> U_1(c) we can infer R(c) -> U_1(c) via biconditional elimination. From R(c) -> U_1(c), u -> U_1(c), R(c) or u we can infer U_1(c) via disjunction elimination. Finally, from w, U_1(c) we can infer w and U_1(c) via conjunction. Therefore, the answer is yes.