Consider the following premises. forall y: P(y) <-> Q(y). exists y: ~Q(y). Can we infer forall y: P(y) from them? If possible, name the inference rules being used at each step.
 From forall y: P(y) <-> Q(y) we can infer forall y: P(y) -> Q(y) via universal biconditional elimination. Finally, from forall y: P(y) -> Q(y), exists y: ~Q(y) we can infer exists y: ~P(y) via existential modus tollens, which contradicts forall y: P(y). Therefore, the answer is no.