Consider the following premises. For all x_7, if x_7 were a mechanic, then x_7 is playing a game. For all x_7, x_7 will play a game if and only if x_7 is a janitor. There is at least one x_7 for which x_7 is a mechanic. Can we infer the following from them? There is at least one x_7 for which x_7 will play a game.
 From the fact that for all x_7, x_7 will play a game if and only if x_7 is a janitor we can infer that for all x_7, if x_7 were a janitor, then x_7 is playing a game. From the fact that there is at least one x_7 for which x_7 is a mechanic we can infer that there is at least one x_7 for which x_7 is a mechanic or x_7 is a janitor. Finally, from the fact that for all x_7, if x_7 were a mechanic, then x_7 is playing a game, that for all x_7, if x_7 were a janitor, then x_7 is playing a game, and that there is at least one x_7 for which x_7 is a mechanic or x_7 is a janitor we can infer that there is at least one x_7 for which x_7 will play a game. Therefore, the answer is yes.