Two prompt γ rays of energies 2020 and 554 keV were observed in coincidence with delayed transitions depopulating the 19/2- isomer in the Z=29, N=42 Cu71 nucleus. The newly identified transitions are proposed to deexcite the 4776- and 5330-keV levels above the 19/2- isomer. Based on the comparison with the low-lying positive-parity states observed in the Z=42, N=50 Mo92 nucleus, spin and parity 23/2- are proposed for the 4776-keV level in Cu71. The high-energy, 2020-keV transition is interpreted as arising from the breaking of the N=40 neutron core. Shell-model calculations with a Ni56 core reproduce the (23/2-)→(19/2-) gap well, suggesting that the 23/2- state is dominated by πp3/2ν((fp)10(g9/2)4) configurations. The present result constitutes further evidence supporting the view that the N=40 subshell closure persists in Cu71, herewith challenging recent suggestions that the coupling of two or more proton or neutron quasiparticles induces a large polarization of the Ni68 core. © 2009 The American Physical Society.