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