  An isotropic component of high energy $\gamma$-ray spectrum measured by Fermi
LAT constrains the proton component of UHECR. The strongest restriction comes
from the highest, $(580-820)$ GeV, energy bin. One more constraint on the
proton component is provided by the IceCube upper bound on ultrahigh energy
cosmogenic neutrino flux. We study the influence of these restrictions on the
source properties, such as evolution and distribution of sources, their energy
spectrum and admixture of nuclei. We also study the sensitivity of restrictions
to various Fermi LAT galactic foreground models (model B being less
restrictive), to the choice of extragalactic background light model and to
overall normalization of the energy spectrum. We claim that the
$\gamma$-ray-cascade constraints are stronger than the neutrino ones, and that
however many proton models are viable. The basic parameters of such models are
relatively large $\gamma_g$ and not very large $z_{\max}$. The allowance for
H$e^4$ admixture also relaxes the restrictions. However we foresee that future
CTA measurements of $\gamma$-ray spectrum at $E_\gamma \simeq (600 - 800)$ GeV,
as well as resolving of more individual $\gamma$-ray sources, may rule out the
proton-dominated cosmic ray models.
