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