Consider the following premises. forall x_7: P_7(x_7) <-> P(x_7). forall x_7: P(x_7) -> W(x_7). forall x_7: Q_4(x_7) -> P(x_7). forall x_7: P_7(x_7) or Q_4(x_7). Can we infer forall x_7: W(x_7) from them? If possible, name the inference rules being used at each step.
 From forall x_7: P_7(x_7) <-> P(x_7) we can infer forall x_7: P_7(x_7) -> P(x_7) via universal biconditional elimination. From forall x_7: P_7(x_7) -> P(x_7), forall x_7: Q_4(x_7) -> P(x_7), forall x_7: P_7(x_7) or Q_4(x_7) we can infer forall x_7: P(x_7) via universal disjunction elimination. Finally, from forall x_7: P(x_7) -> W(x_7), forall x_7: P(x_7) we can infer forall x_7: W(x_7) via universal modus ponens. Therefore, the answer is yes.