[en] We present an analysis of the intrinsic (unattenuated by the extragalactic background light, EBL) power-law spectral indices of 128 extragalactic sources detected up to $z\sim <!--\; ???\; -->2$ with the Fermi-Large Area Telescope (LAT) at very high energies (VHEs, $E⩾<!--\; ???\; -->50$ GeV). The median of the intrinsic index distribution is 2.20 (versus 2.54 for the observed distribution). We also analyze the observed spectral breaks (i.e., the difference between the VHE and high energy, HE, $100\mathrm{M}\mathrm{e}\mathrm{V}⩽<!--\; ???\; -->E⩽<!--\; ???\; -->300\mathrm{G}\mathrm{e}\mathrm{V},$ spectral indices). The Fermi-LAT has now provided a large sample of sources detected both at VHE and HE with comparable exposure that allows us to test models of extragalactic γ-ray photon propagation. We find that our data are compatible with simulations that include intrinsic blazar curvature and EBL attenuation. There is also no evidence of evolution with redshift of the physics that drives the photon emission in high-frequency synchrotron peak (HSP) blazars. This makes HSP blazars excellent probes of the EBL.