Cartesian product of sets of sets

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If I have two sets A, B, which are sets of sets. Is there any abbreviated notation to write $$ \{ C \times D | C \in A \wedge D \in B\} $$ ?

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You can use $S = \{C \times D\;|\;C \in A \land D \in B\}$ and use $S$ or define $S[A:B]$ to mean that.