I'm wondering if it's right (and not abusive or ugly) the use of two, or more, "such that" in a definition, and in the dealing with mathematical objects. I know that I could find equivalences for such definitions, and some of them more beautiful and readable; but I want to know if such use is correct.
As an example: Let A, B be sets.
$\mathcal{F}(A;B):=\Big\{f: \Big(f\subset A\times B : \; [(a,b)\in f \wedge (a,c)\in f] \Leftrightarrow b=c \Big)\Big\}$.