Consider the following premises. For all x_7, x_7 is a mechanic or x_7 will drink water. For all x_7, if x_7 drinks water, then x_7 is sad. For all x_7, x_7 is not sad. There is at least one x_7 for which x_7 is not a mechanic or x_7 will cook. Can we infer the following from them? If we can, name the inference rule being used: For all x_7, x_7 is not sad.
That is one of the premises. Therefore, the answer is yes.