Consider the following premises. Mary is a mechanic if and only if Elisabeth is not an electrician. For all x_23, x_23 will go running. If Elisabeth were an electrician, then Robert is not running. Can we infer the following from them? If we can, name the inference rule being used: Mary is a mechanic.
 From the fact that for all x_23, x_23 will go running we can infer that Robert is running via universal instantiation. From the fact that if Elisabeth were an electrician, then Robert is not running, and that Robert is running we can infer that Elisabeth is not an electrician via modus tollens. From the fact that Mary is a mechanic if and only if Elisabeth is not an electrician we can infer that if Elisabeth were not an electrician, then Mary is a mechanic via biconditional elimination. Finally, from the fact that if Elisabeth were not an electrician, then Mary is a mechanic, and that Elisabeth is not an electrician we can infer that Mary is a mechanic via modus ponens. Therefore, the answer is yes.