Consider the following premises. ~T_4(a_7). forall y: T(y) <-> T_4(y). T(a_7) <-> q. Can we infer q from them? If possible, name the inference rules being used at each step.
 From forall y: T(y) <-> T_4(y) we can infer T(a_7) <-> T_4(a_7) via universal instantiation. From T(a_7) <-> T_4(a_7), ~T_4(a_7) we can infer ~T(a_7) via biconditional elimination. Finally, from T(a_7) <-> q, ~T(a_7) we can infer ~q via biconditional elimination, which contradicts q. Therefore, the answer is no.