**Proof**: *(related to "Justification of the Set Intersection")*

- Let $A$ and $B$ be sets.
- By the axiom of separation there is a set $\{z\in A \mid z\in B\}.$
- The axiom of extensionality ensures the uniqueness of such a set.
- This set is exactly the set intersection $A\cap B.$

q.e.d

| | | | Contributors: *bookofproofs* | References: [656], [983]

(none)

[983] **Ebbinghaus, H.-D.**: “Einführung in die Mengenlehre”, BI Wisschenschaftsverlag, 1994, 3

[656] **Hoffmann, Dirk W.**: “Grenzen der Mathematik – Eine Reise durch die Kerngebiete der mathematischen Logik”, Spektrum Akademischer Verlag, 2011

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