Consider the following premises. For all x_6, if x_6 were a cashier, then x_6 is an electrician. For all x_6, x_6 is an electrician if and only if x_6 is an astronaut. For all x_6, if x_6 were an astronaut, then x_6 is a cashier. For all x_6, x_6 is not an electrician. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_6 for which x_6 is an astronaut.
 From the fact that for all x_6, if x_6 were an astronaut, then x_6 is a cashier, and that for all x_6, if x_6 were a cashier, then x_6 is an electrician we can infer that for all x_6, if x_6 were an astronaut, then x_6 is an electrician via universal transitivity. From the fact that for all x_6, x_6 is an electrician if and only if x_6 is an astronaut we can infer that for all x_6, if x_6 were an electrician, then x_6 is an astronaut via universal biconditional elimination. From the fact that for all x_6, if x_6 were an electrician, then x_6 is an astronaut, and that for all x_6, if x_6 were an astronaut, then x_6 is an electrician we can infer that for all x_6, x_6 is an electrician if and only if x_6 is an astronaut via universal biconditional introduction. Finally, from the fact that for all x_6, x_6 is an electrician if and only if x_6 is an astronaut, and that for all x_6, x_6 is not an electrician we can infer that for all x_6, x_6 is not an astronaut via universal biconditional elimination, which contradicts that There is at least one x_6 for which x_6 is an astronaut. Therefore, the answer is no.