Usage of "such that" in logical statements

Question

I have a simple question about the usage of "such that" in logical statements.

Let the statement S be: "For every $x \in A, f (x) > 5$."

In the negation of S:

There is an $x \in A$ such that $f (x) ≤ 5$.

The comma in S is converted to "such that" in the negation of S.

Can somebody clarify on the "such that" came in the negation of S.

Answer 1

Rubik is right: There is an implied "such that" in the first statement as well.

For every $x\in A$, $f(x)>5$ means $\forall\,x$ such that $x\in A$, $f(x)>5$, which in turn can be translated to $\forall\,x\quad x\in A\implies f(x)>5$.