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