Consider the following premises. ~S_7(a_7). q <-> T_4(a_7). forall x_7: T_4(x_7) <-> S_7(x_7). Can we infer ~q from them? If possible, name the inference rules being used at each step.
 From forall x_7: T_4(x_7) <-> S_7(x_7) we can infer T_4(a_7) <-> S_7(a_7) via universal instantiation. From T_4(a_7) <-> S_7(a_7), ~S_7(a_7) we can infer ~T_4(a_7) via biconditional elimination. Finally, from q <-> T_4(a_7), ~T_4(a_7) we can infer ~q via biconditional elimination. Therefore, the answer is yes.