Consider the following premises. exists x_2: P(x_2) <-> R_3(x_2). forall x_2: Q(x_2) <-> R_3(x_2). Can we infer exists x_2: P(x_2) -> Q(x_2) from them? If possible, name the inference rules being used at each step.
 From forall x_2: Q(x_2) <-> R_3(x_2) we can infer forall x_2: R_3(x_2) -> Q(x_2) via universal biconditional elimination. From exists x_2: P(x_2) <-> R_3(x_2) we can infer exists x_2: P(x_2) -> R_3(x_2) via existential biconditional elimination. Finally, from exists x_2: P(x_2) -> R_3(x_2), forall x_2: R_3(x_2) -> Q(x_2) we can infer exists x_2: P(x_2) -> Q(x_2) via existential transitivity. Therefore, the answer is yes.