Consider the following premises. For all z, z is a mechanic if and only if z is happy. For all z, z will play tennis or z is happy. For all z, if z plays tennis, then z is a mechanic. Can we infer the following from them? There is at least one z for which z is not a mechanic.
 From the fact that for all z, z is a mechanic if and only if z is happy we can infer that for all z, if z were happy, then z is a mechanic. Finally, from the fact that for all z, if z plays tennis, then z is a mechanic, that for all z, if z were happy, then z is a mechanic, and that for all z, z will play tennis or z is happy we can infer that for all z, z is a mechanic, which contradicts that There is at least one z for which z is not a mechanic. Therefore, the answer is no.