Consider the following premises. There is at least one x for which if x were an electrician, then x is playing a game. For all x, x will play a game if and only if x will sleep. For all x, if x sleeps, then x is an electrician. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x for which if x were an electrician, then x is playing a game.
That is one of the premises. Therefore, the answer is yes.