Corollary 2

The product of a finite family $(\mathfrak{a}_i)_{i \in \mathrm{I}}$ of non-zero cardinals, of which the greatest is an infinite cardinal $\mathfrak{a}$, is equal to $\mathfrak{a}$.

Let $\mathfrak{b}$ denote the product and let $n$ be the number of elements in I. Then $\mathfrak{b} \leqslant \mathfrak{a}^n = \mathfrak{a}$ (§ 3, no. 6, Proposition 14). On the other hand, since $\mathfrak{a}_i \geqslant 1$ for all $i \in \mathrm{I}$, we have $\mathfrak{b} \geqslant \mathfrak{a}$ (§ 3, no. 6, Proposition 14).