  Predicting magic wavelengths accurately requires precise knowledge of
electric-dipole matrix elements of nearby atomic transitions. As a result,
measurements of magic wavelengths allow us to test theoretical predictions for
the matrix elements that frequently can not be probed by any other methods.
Here, we calculate and measure a magic wavelength near $473$ nm of the
$5s^2\,^1\!S_0 - 5s5p\,^3\!P_1$ intercombination transition of ${}^{88}$Sr.
Experimentally, we find $473.361(4)$ nm for $\Delta m=0$ ($\pi$ transition) and
$473.133(14)$ nm for $\Delta m=-1$ ($\sigma^{-}$ transition). Theoretical
calculations yield $473.375(22)$~nm and $473.145(20)$ nm, respectively. The
$^3\!P_1$ polarizability is dominated by the contributions to the $5p^2\,
^3\!P$ levels and excellent agreement of theory and experiment validates both
theoretical values of these matrix elements and estimates of their
uncertainties.
