Consider the following premises. exists x_13: P_13(x_13) <-> Q_13(x_13). forall x_13: Q_13(x_13) <-> T(x_13). forall x_13: ~P_13(x_13). forall x_13: T(x_13) <-> P_3(x_13). Can we infer exists x_13: ~P_3(x_13) from them? If possible, name the inference rules being used at each step.
 From exists x_13: P_13(x_13) <-> Q_13(x_13), forall x_13: ~P_13(x_13) we can infer exists x_13: ~Q_13(x_13) via existential biconditional elimination. From forall x_13: Q_13(x_13) <-> T(x_13), exists x_13: ~Q_13(x_13) we can infer exists x_13: ~T(x_13) via existential biconditional elimination. Finally, from forall x_13: T(x_13) <-> P_3(x_13), exists x_13: ~T(x_13) we can infer exists x_13: ~P_3(x_13) via existential biconditional elimination. Therefore, the answer is yes.