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 $x \ne a$...".

The exact correspondence in first order language is as follows:

$∀x((x∈S ∧ x≠a) → ⋯)$

It reads: for all $x$, if $x$ belongs to $S$ and $x$ is not $a$, then....

$x≠a$ is just a short form for $(x=a)$