= Universal evaluation phantom map
Choose one representative of each <finite spectrum> and form $X=\bigvee_{(F,u:F\to D)}F$. Let $e:X\to D$ evaluate each summand and let $p:D\to\operatorname{cofib}(e)$. Every map from a <finite spectrum> factors through its corresponding summand, so $p$ is a <phantom map of spectra>. If $p=0$, exactness supplies a section of $e$, making $D$ a <retract> of $X$. Consequently a spectrum that is not a retract of any wedge of finite spectra has a nonzero such phantom.
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