Consider the following premises. For all x_13, if x_13 writes a letter, then x_13 is bored. For all x_13, if x_13 were a mechanic, then x_13 is playing a game. For all x_13, x_13 is bored or x_13 will not play a game. For all x_13, x_13 will write a letter. There is at least one x_13 for which if x_13 sleeps, then x_13 is a mechanic. Can we infer the following from them? For all x_13, if x_13 writes a letter, then x_13 is bored.
That is one of the premises. Therefore, the answer is yes.