Consider the following premises. exists x_10: P(x_10) or ~Q_10(x_10). forall x_10: P(x_10) <-> Q_10(x_10). Can we infer exists x_10: Q_10(x_10) -> P(x_10) from them? If possible, name the inference rules being used at each step.
 From forall x_10: P(x_10) <-> Q_10(x_10) we can infer forall x_10: P(x_10) -> Q_10(x_10) via universal biconditional elimination. Finally, from exists x_10: P(x_10) or ~Q_10(x_10) we can infer exists x_10: Q_10(x_10) -> P(x_10) via existential rewriting. Therefore, the answer is yes.