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