Consider the following premises. For all x_2, if x_2 were an electrician, then x_2 is a sailor. There is at least one x_2 for which if x_2 were a sailor, then x_2 is bored. For all x_2, if x_2 were bored, then x_2 is an electrician. Can we infer the following from them? If we can, name the inference rule being used: For all x_2, if is not true that x_2 is an electrician if and only if x_2 is bored.
 From the fact that for all x_2, if x_2 were an electrician, then x_2 is a sailor, and that there is at least one x_2 for which if x_2 were a sailor, then x_2 is bored we can infer that there is at least one x_2 for which if x_2 were an electrician, then x_2 is bored via existential transitivity. Finally, from the fact that there is at least one x_2 for which if x_2 were an electrician, then x_2 is bored, and that for all x_2, if x_2 were bored, then x_2 is an electrician we can infer that there is at least one x_2 for which x_2 is an electrician if and only if x_2 is bored via existential biconditional introduction, which contradicts that For all x_2, if is not true that x_2 is an electrician if and only if x_2 is bored. Therefore, the answer is no.