Consider the following premises. forall y: U_2(y) -> U(y). forall y: U_2(y). forall y: Q(y) and R(y). Can we infer forall y: U(y) and Q(y) from them? If possible, name the inference rules being used at each step.
 From forall y: U_2(y) -> U(y), forall y: U_2(y) we can infer forall y: U(y) via universal modus ponens. From forall y: Q(y) and R(y) we can infer forall y: Q(y) via universal simplification. Finally, from forall y: U(y), forall y: Q(y) we can infer forall y: U(y) and Q(y) via universal conjunction. Therefore, the answer is yes.