Consider the following premises. forall y: T_2(y) <-> R(y). forall y: T(y). exists y: T_2(y) -> ~T(y). Can we infer exists y: ~R(y) from them? If possible, name the inference rules being used at each step.
 From exists y: T_2(y) -> ~T(y), forall y: T(y) we can infer exists y: ~T_2(y) via existential modus tollens. Finally, from forall y: T_2(y) <-> R(y), exists y: ~T_2(y) we can infer exists y: ~R(y) via existential biconditional elimination. Therefore, the answer is yes.