Consider the following premises. exists x: S_3(x) <-> W(x). forall x: W(x). forall x: S(x). Can we infer exists x: S(x) and S_3(x) from them? If possible, name the inference rules being used at each step.
 From exists x: S_3(x) <-> W(x) we can infer exists x: W(x) -> S_3(x) via existential biconditional elimination. From exists x: W(x) -> S_3(x), forall x: W(x) we can infer exists x: S_3(x) via existential modus ponens. Finally, from forall x: S(x), exists x: S_3(x) we can infer exists x: S(x) and S_3(x) via existential conjunction. Therefore, the answer is yes.