Consider the following premises. For all x_4, x_4 is happy if and only if x_4 is a sailor. There is at least one x_4 for which x_4 is a sailor. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_4 for which x_4 is happy.
 From the fact that for all x_4, x_4 is happy if and only if x_4 is a sailor we can infer that for all x_4, if x_4 were a sailor, then x_4 is happy via universal biconditional elimination. Finally, from the fact that for all x_4, if x_4 were a sailor, then x_4 is happy, and that there is at least one x_4 for which x_4 is a sailor we can infer that there is at least one x_4 for which x_4 is happy via existential modus ponens. Therefore, the answer is yes.