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