Consider the following premises. forall x_4: Q_4(x_4) -> R_4(x_4). forall x_4: R(x_4) -> Q_4(x_4). forall x_4: R_4(x_4) -> R(x_4). Can we infer R(f) -> R_4(f) from them?
 From forall x_4: R(x_4) -> Q_4(x_4), forall x_4: Q_4(x_4) -> R_4(x_4) we can infer forall x_4: R(x_4) -> R_4(x_4). From forall x_4: R(x_4) -> R_4(x_4), forall x_4: R_4(x_4) -> R(x_4) we can infer forall x_4: R(x_4) <-> R_4(x_4). From forall x_4: R(x_4) <-> R_4(x_4) we can infer R(f) <-> R_4(f). Finally, from R(f) <-> R_4(f) we can infer R(f) -> R_4(f). Therefore, the answer is yes.