Consider the following premises. t <-> q. U(j) <-> t. forall x_13: ~P_13(x_13). forall x_13: P_13(x_13) <-> U(x_13). Can we infer ~q from them? If possible, name the inference rules being used at each step.
 From forall x_13: P_13(x_13) <-> U(x_13), forall x_13: ~P_13(x_13) we can infer forall x_13: ~U(x_13) via universal biconditional elimination. From forall x_13: ~U(x_13) we can infer ~U(j) via universal instantiation. From U(j) <-> t, ~U(j) we can infer ~t via biconditional elimination. Finally, from t <-> q, ~t we can infer ~q via biconditional elimination. Therefore, the answer is yes.