We report the first confirmation of the predicted inversion between the pi2p3/2 and pi1f5/2 nuclear states in the nu(g)9/2 midshell. This was achieved at the ISOLDE facility, by using a combination of in-source laser spectroscopy and collinear laser spectroscopy on the ground states of 71,73,75Cu, which measured the nuclear spin and magnetic moments. The obtained values are mu(71Cu)=+2.2747(8)mu(N), mu(73Cu)=+1.7426(8)mu(N), and mu(75Cu)=+1.0062(13)mu(N) corresponding to spins I=3/2 for 71,73Cu and I=5/2 for 75Cu. The results are in fair agreement with large-scale shell-model calculations.