Symbolic predicate logic for "for all elements in a set except this one..." How would a statement beginning, "For all $x$ in set $S$ except $x=a$..." be translated into symbolic predicate logic? I'm somewhat of a purist in symbols and am less than satisfied with "$\forall x \in S$ except $x = a$..." or "$\forall x \in S$ where $x \ne a$...".
$$\forall x \in S\setminus \{a\}, \,\,\,\ldots$$
I would use $(\exists a\in S)(\forall x\in S)(x\neq a \Leftrightarrow \cdots)$.  It's not a direct correspondence to the English, but not everything in symbolic logic is.