In the last chapter of his Concise course in algebraic topology, May states (without proof or reference) that for an arbitrary collection $(X_i)_{i\in I}$ of spectra the following hold:
$\pi_n(\prod_{i\in I} X_i)=\prod_{i\in I} \pi_n(X_i)$
$\pi_n(\bigvee_{i\in I} X_i)=\sum_{i\in I} \pi_n(X_i)$
The first one is clear, since the same holds for spaces. But the homotopy of a wedge sum can be quite complicated in general, doesn't it? Is this an exclusive property of spectra? Why does it hold?