Consider the following premises. exists y_2: T_4(y_2) or T_3(y_2). forall y_2: T_4(y_2) <-> T(y_2). forall y_2: ~T(y_2). Can we infer exists y_2: T_3(y_2) from them? If possible, name the inference rules being used at each step.
 From forall y_2: T_4(y_2) <-> T(y_2), forall y_2: ~T(y_2) we can infer forall y_2: ~T_4(y_2) via universal biconditional elimination. Finally, from exists y_2: T_4(y_2) or T_3(y_2), forall y_2: ~T_4(y_2) we can infer exists y_2: T_3(y_2) via existential disjunctive syllogism. Therefore, the answer is yes.