Help with notation for set definition: $\{ j : A_j \in A_1\}$

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$\{ j : A_j \in A_1\}$ where $A_1, A_2, A_3, A_4$ are defined.

I understand the elementary notation but can't quite see how the set is supposed to be defined. Is this supposed to be the set of all the defined sets above which are in $A_1$?