Consider the following premises. For all x, if x plays squash, then x is a politician. For all x, if x were a sailor, then x is a politician. For all x, if x were a politician, then x is a sailor. Can we infer the following from them? If we can, name the inference rule being used: For all x, if x plays squash, then x is a sailor.
 From the fact that for all x, if x were a politician, then x is a sailor, and that for all x, if x were a sailor, then x is a politician we can infer that for all x, x is a politician if and only if x is a sailor via universal biconditional introduction. From the fact that for all x, x is a politician if and only if x is a sailor we can infer that for all x, if x were a politician, then x is a sailor via universal biconditional elimination. Finally, from the fact that for all x, if x plays squash, then x is a politician, and that for all x, if x were a politician, then x is a sailor we can infer that for all x, if x plays squash, then x is a sailor via universal transitivity. Therefore, the answer is yes.