Consider the following premises. forall x_5: P_5(x_5) -> R(x_5). exists x_5: P_5(x_5) <-> Q(x_5). Can we infer exists x_5: Q(x_5) -> R(x_5) from them?
 From exists x_5: P_5(x_5) <-> Q(x_5) we can infer exists x_5: Q(x_5) -> P_5(x_5). Finally, from exists x_5: Q(x_5) -> P_5(x_5), forall x_5: P_5(x_5) -> R(x_5) we can infer exists x_5: Q(x_5) -> R(x_5). Therefore, the answer is yes.