Collisions of high energy cosmic rays with intergalactic gas produce various secondaries, including neutral pions that decay into high energy γ rays. The Landau-Milekhin hydrodynamical model for proton-proton collisions is used to calculate the pion production spectrum corresponding to cosmic γ rays of energy above 10 Gev. A source function for these high energy γ rays in space is found by combining the pion production and decay spectra with the primary cosmic ray proton flux. The resulting γ ray spectrum follows a different power law than spectra based upon the usual assumption of a line spectrum for the pions in the center of mass system of the colliding protons. The high energy γ ray intensity in space is calculated for a simple model universe. By comparison with previous estimates for the proton photoproduction process, it is found that proton-proton and proton-photon collisions appear to contribute about the same order of magnitude to the intergalactic γ ray intensity above ∼1016 eV.