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