Consider the following premises. For all x_12, x_12 will climb a mountain if and only if x_12 is happy. Joseph is happy if and only if it is late. For all x_12, x_12 is an electrician if and only if x_12 will climb a mountain. For all x_12, x_12 is not an electrician. Can we infer the following from them? If we can, name the inference rule being used: It is not late.
 From the fact that for all x_12, x_12 is an electrician if and only if x_12 will climb a mountain, and that for all x_12, x_12 is not an electrician we can infer that for all x_12, x_12 will not climb a mountain via universal biconditional elimination. From the fact that for all x_12, x_12 will climb a mountain if and only if x_12 is happy, and that for all x_12, x_12 will not climb a mountain we can infer that for all x_12, x_12 is not happy via universal biconditional elimination. From the fact that for all x_12, x_12 is not happy we can infer that Joseph is not happy via universal instantiation. Finally, from the fact that Joseph is happy if and only if it is late, and that Joseph is not happy we can infer that it is not late via biconditional elimination. Therefore, the answer is yes.