Consider the following premises. For all x_10, x_10 is a lawyer if and only if x_10 is an office clerk. If it is sunny, then William is a lawyer. William is an office clerk. Can we infer the following from them? If we can, name the inference rule being used: William is a lawyer.
 From the fact that for all x_10, x_10 is a lawyer if and only if x_10 is an office clerk we can infer that William is a lawyer if and only if William is an office clerk via universal instantiation. From the fact that William is an office clerk we can infer that William is an office clerk or it is sunny via addition. From the fact that William is a lawyer if and only if William is an office clerk we can infer that if William were an office clerk, then William is a lawyer via biconditional elimination. Finally, from the fact that if William were an office clerk, then William is a lawyer, that if it is sunny, then William is a lawyer, and that William is an office clerk or it is sunny we can infer that William is a lawyer via disjunction elimination. Therefore, the answer is yes.