Consider the following premises. forall x_10: Q_6(x_10) -> P_10(x_10). forall x_10: P_10(x_10) <-> U(x_10). forall x_10: U(x_10). forall x_10: U(x_10) -> P_10(x_10). Can we infer forall x_10: P_10(x_10) from them? If possible, name the inference rules being used at each step.
 From forall x_10: P_10(x_10) <-> U(x_10) we can infer forall x_10: P_10(x_10) -> U(x_10) via universal biconditional elimination. From forall x_10: U(x_10) we can infer forall x_10: U(x_10) or Q_6(x_10) via universal addition. From forall x_10: P_10(x_10) -> U(x_10), forall x_10: U(x_10) -> P_10(x_10) we can infer forall x_10: P_10(x_10) <-> U(x_10) via universal biconditional introduction. From forall x_10: P_10(x_10) <-> U(x_10) we can infer forall x_10: U(x_10) -> P_10(x_10) via universal biconditional elimination. Finally, from forall x_10: U(x_10) -> P_10(x_10), forall x_10: Q_6(x_10) -> P_10(x_10), forall x_10: U(x_10) or Q_6(x_10) we can infer forall x_10: P_10(x_10) via universal disjunction elimination. Therefore, the answer is yes.