Consider the following premises. exists x: Q(x). forall x: Q_1(x) <-> T(x). forall x: Q_1(x). Can we infer exists x: Q(x) and T(x) from them? If possible, name the inference rules being used at each step.
 From forall x: Q_1(x) <-> T(x) we can infer forall x: Q_1(x) -> T(x) via universal biconditional elimination. From forall x: Q_1(x) -> T(x), forall x: Q_1(x) we can infer forall x: T(x) via universal modus ponens. Finally, from exists x: Q(x), forall x: T(x) we can infer exists x: Q(x) and T(x) via existential conjunction. Therefore, the answer is yes.