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