Consider the following premises. For all x_7, x_7 is happy. For all x_7, if x_7 were fast, then x_7 is a lawyer. For all x_7, x_7 is happy if and only if x_7 is fast. Can we infer the following from them? If we can, name the inference rule being used: For all x_7, x_7 is a lawyer.
 From the fact that for all x_7, x_7 is happy if and only if x_7 is fast we can infer that for all x_7, if x_7 were happy, then x_7 is fast via universal biconditional elimination. From the fact that for all x_7, if x_7 were happy, then x_7 is fast, and that for all x_7, if x_7 were fast, then x_7 is a lawyer we can infer that for all x_7, if x_7 were happy, then x_7 is a lawyer via universal transitivity. Finally, from the fact that for all x_7, if x_7 were happy, then x_7 is a lawyer, and that for all x_7, x_7 is happy we can infer that for all x_7, x_7 is a lawyer via universal modus ponens. Therefore, the answer is yes.