Consider the following premises. For all x_2, if x_2 writes a letter, then x_2 is fast. For all x_2, if x_2 were sad, then x_2 is writing a letter. For all x_2, if x_2 were fast, then x_2 is sad. Can we infer the following from them? There is at least one x_2 for which the fact that x_2 writes a letter does not imply that x_2 is sad.
 From the fact that for all x_2, if x_2 writes a letter, then x_2 is fast, and that for all x_2, if x_2 were fast, then x_2 is sad we can infer that for all x_2, if x_2 writes a letter, then x_2 is sad. From the fact that for all x_2, if x_2 were sad, then x_2 is writing a letter, and that for all x_2, if x_2 writes a letter, then x_2 is sad we can infer that for all x_2, x_2 is sad if and only if x_2 will write a letter. Finally, from the fact that for all x_2, x_2 is sad if and only if x_2 will write a letter we can infer that for all x_2, if x_2 writes a letter, then x_2 is sad, which contradicts that There is at least one x_2 for which the fact that x_2 writes a letter does not imply that x_2 is sad. Therefore, the answer is no.