Consider the following premises. For all x, x will work if and only if x is sad. For all x, if x were sad, then x is writing a letter. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x for which the fact that x works does not imply that x is writing a letter.
 From the fact that for all x, x will work if and only if x is sad we can infer that for all x, if x works, then x is sad via universal biconditional elimination. Finally, from the fact that for all x, if x works, then x is sad, and that for all x, if x were sad, then x is writing a letter we can infer that for all x, if x works, then x is writing a letter via universal transitivity, which contradicts that There is at least one x for which the fact that x works does not imply that x is writing a letter. Therefore, the answer is no.