Consider the following premises. For all x_6, if x_6 were an electrician, then x_6 is playing squash. For all x_6, if x_6 writes a letter, then x_6 is running. For all x_6, if x_6 goes running, then x_6 is an electrician. There is at least one x_6 for which x_6 will not play squash. Can we infer the following from them? If we can, name the inference rule being used: For all x_6, x_6 will write a letter.
 From the fact that for all x_6, if x_6 were an electrician, then x_6 is playing squash, and that there is at least one x_6 for which x_6 will not play squash we can infer that there is at least one x_6 for which x_6 is not an electrician via existential modus tollens. From the fact that for all x_6, if x_6 writes a letter, then x_6 is running, and that for all x_6, if x_6 goes running, then x_6 is an electrician we can infer that for all x_6, if x_6 writes a letter, then x_6 is an electrician via universal transitivity. Finally, from the fact that for all x_6, if x_6 writes a letter, then x_6 is an electrician, and that there is at least one x_6 for which x_6 is not an electrician we can infer that there is at least one x_6 for which x_6 will not write a letter via existential modus tollens, which contradicts that For all x_6, x_6 will write a letter. Therefore, the answer is no.