Consider the following premises. forall x_6: P_6(x_6) -> Q_6(x_6). exists x_6: Q_6(x_6) -> R_6(x_6). forall x_6: P_6(x_6) and Q_3(x_6). Can we infer exists x_6: R_6(x_6) from them? If possible, name the inference rules being used at each step.
 From forall x_6: P_6(x_6) -> Q_6(x_6), exists x_6: Q_6(x_6) -> R_6(x_6) we can infer exists x_6: P_6(x_6) -> R_6(x_6) via existential transitivity. From forall x_6: P_6(x_6) and Q_3(x_6) we can infer forall x_6: P_6(x_6) via universal simplification. Finally, from exists x_6: P_6(x_6) -> R_6(x_6), forall x_6: P_6(x_6) we can infer exists x_6: R_6(x_6) via existential modus ponens. Therefore, the answer is yes.