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

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 $A,B\in\mathcal F$.

Browsing through Internet I could find only finite and uncountable versions of the Sunflower Lemma (but not the countable one).