Please help me to find a proper reference to the following infinite version of the Sunflower Lemma.



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> **Lemma.** Let $n\in\mathbb N$. Every infinite family of $n$-element sets contains an infinite subfamily $\mathcal F$ such that $A\cap B=\bigcap\mathcal F$ for any distinct sets $A,B\in\mathcal F$.
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Browsing through Internet I could find only finite and uncountable versions of the Sunflower Lemma (but not the countable one).



A reference to infinite version of the Sunflower Lemma
I found it in the book Komjáth, Péter; Totik, Vilmos, [**Problems and theorems in classical set theory**](http://dx.doi.org/10.1007/0-387-36219-3), Problem Books in Mathematics. New York, NY: Springer (ISBN 0-387-30293-X/hbk). xii, 514 p. (2006). [ZBL1103.03041](https://zbmath.org/?q=an:1103.03041). It's stated on p. 107 as the first item in the chapter on $\Delta$-systems:



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> 1. An infinite family of $n$-element sets ($n\lt\omega$) includes an infinite $\Delta$-subfamily.
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A proof is given on p. 421. No reference is given.


