What does this vertical line mean after X?

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Natalie1
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  • Y = {X | X ∉ X}, the set of all X such that X is not an element of X, written in set-builder notation.
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Hi Natalie! Welcome to MHB! (Smile)

The vertical line means: "for which holds that".
So it reads as: the set of all X for which holds that X is not an element of itself.

It's part of the set-builder-notation.
 
While equivalent to what I like Serena posted, I was taught (in the context of set builder notation) it means "such that." :)