Consider the following premises. For all z, if z climbs a mountain, then z is a mechanic. For all z, if z climbs a mountain, then z is a mechanic. For all z, if z were a mechanic, then z is climbing a mountain. Can we infer the following from them? If we can, name the inference rule being used: There is at least one z for which the fact that z climbs a mountain does not imply that z is a mechanic.
 From the fact that for all z, if z climbs a mountain, then z is a mechanic, and that for all z, if z were a mechanic, then z is climbing a mountain we can infer that for all z, z will climb a mountain if and only if z is a mechanic via universal biconditional introduction. From the fact that for all z, z will climb a mountain if and only if z is a mechanic we can infer that for all z, if z were a mechanic, then z is climbing a mountain via universal biconditional elimination. From the fact that for all z, if z were a mechanic, then z is climbing a mountain, and that for all z, if z climbs a mountain, then z is a mechanic we can infer that for all z, z is a mechanic if and only if z will climb a mountain via universal biconditional introduction. Finally, from the fact that for all z, z is a mechanic if and only if z will climb a mountain we can infer that for all z, if z climbs a mountain, then z is a mechanic via universal biconditional elimination, which contradicts that There is at least one z for which the fact that z climbs a mountain does not imply that z is a mechanic. Therefore, the answer is no.