Need help with a symbol that appears in logic notations, as it appears (for the first time, in the book) on page 2 of the book : Elements of Real Analysis, by Denlinger.
The logical statement containing the symbol is stated below with its interpretation in the book:
Existential Qualifier : $\exists \,\ x \in A$ 'symbol' $P(x)$
If $P(x)$ is a statement about $x$, and $A$ is a set, then $"\exists x \in A,$ 'symbol' $ P(x)"$ is the statement, "There exists at least one element in the set $A$ such that $P(x)$ is true."
My interpretation is that it is same as: $":"$ or $"|"$, that also mean : "such that"; but worry if am correct or not.
Also, the book never uses the symbols: $":"$ or $"|"$, & is always using instead the given symbol, whenever the meaning needed is : "such that".
If correct, then is there such symbol available in MathJax?
Edit :
As per the comment by @MinusOne-Twelfth, it is listed as second symbol, by Detexify, as shown below:
