Question regarding syntax of $\bigcap$ definition I know what this definition is supposed to do. However just looking at the syntax, i cannot explain it to myself.
$$
\bigcap M := \{x \mid \forall y \in M : x \in y\}
$$
Could somebody please explain me how to read this definition (not what it does, but rather how to read it close to the definition's syntax so that it is easier to understand)?

It would be easier to see it this way: Let $A$ and $B$ be sets. Let $M=\{A,B\}.$ Define $$\bigcap M = \bigcap_{y\in M} y.$$
Then $\bigcap M = A \cap B,$ and if you expand the definition above you can see that it fits the one you provided.
