Consider the following premises. David is a mechanic or Patricia is working. For all x_7, x_7 is a mechanic if and only if x_7 is a lawyer. If Patricia works, then David is a lawyer. Can we infer the following from them? If we can, name the inference rule being used: David is not a lawyer.
 From the fact that for all x_7, x_7 is a mechanic if and only if x_7 is a lawyer we can infer that David is a mechanic if and only if David is a lawyer via universal instantiation. From the fact that David is a mechanic if and only if David is a lawyer we can infer that if David were a mechanic, then David is a lawyer via biconditional elimination. Finally, from the fact that if David were a mechanic, then David is a lawyer, that if Patricia works, then David is a lawyer, and that David is a mechanic or Patricia is working we can infer that David is a lawyer via disjunction elimination, which contradicts that David is not a lawyer. Therefore, the answer is no.