In this letter we present the result of the cross correlation between the 4th INTEGRAL/IBIS soft gamma-ray catalog, in the range 20-100 keV, and the Fermi LAT bright source list of objects emitting in the 100 MeV - 100 GeV range. The main result is that only a minuscule part of the more than 720 sources detected by INTEGRAL and the population of 205 Fermi LAT sources are detected in both spectral regimes. This is in spite of the mCrab INTEGRAL sensitivity for both galactic and extragalactic sources and the breakthrough, in terms of sensitivity, achieved by Fermi at MeV-GeV energies. The majority of the 14 Fermi LAT sources clearly detected in the 4th INTEGRAL/IBIS catalog are optically identified AGNs (10) complemented by 2 isolated pulsars (Crab and Vela) and 2 High Mass X-Ray Binaries (HMXB, LS I +61 303 and LS 5039). Two more possible associations have been found: one is 0FGL J1045.6-5937, possibly the counterpart at high energy of the massive colliding wind binary system Eta Carinae, discovered to be a soft gamma ray emitter by recent INTEGRAL observations and 0FGL J1746.0-2900 coincident with IGR J17459-2902, but still not identified with any known object at lower energy. For the remaining 189 Fermi LAT sources no INTEGRAL counterpart was found and we report the 2 sigma upper limit in the energy band 20-40 keV. ; Comment: Accepted for publication in ApJL, 3 figures, 2 tables