Consider the following premises. For all x, if x were a scientist, then x is writing a letter. There is at least one x for which x is a scientist if and only if x will write a letter. Can we infer the following from them? There is at least one x for which if x were a scientist, then x is writing a letter.
 From the fact that there is at least one x for which x is a scientist if and only if x will write a letter we can infer that there is at least one x for which if x writes a letter, then x is a scientist. From the fact that there is at least one x for which if x writes a letter, then x is a scientist, and that for all x, if x were a scientist, then x is writing a letter we can infer that there is at least one x for which x will write a letter if and only if x is a scientist. Finally, from the fact that there is at least one x for which x will write a letter if and only if x is a scientist we can infer that there is at least one x for which if x were a scientist, then x is writing a letter. Therefore, the answer is yes.