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A novel isochronous mass spectrometry, termed as $Bρ$-defined IMS, is established at the experimental cooler-storage ring CSRe in Lanzhou. Its potential has been studied through high precision mass measurements of $^{58}$Ni projectile fragments. Two time-of-flight detectors were installed in one of the straight sections of CSRe, thus enabling simultaneous measurements of the velocity and the revolution time of each stored short-lived ion. This allows for calculating the magnetic rigidity $Bρ$ and the orbit length $C$ of each ion. The accurate $Bρ(C)$ function has been constructed, which is a universal calibration curve used to deduce the masses of the stored nuclides. The sensitivity to single stored ions, quickness, and background-free characteristics of the method are ideally suited to address nuclides with very short lifetimes and tiniest production yields. In the limiting case of just a single particle, the attained mass resolving power allows one us to determine its mass-over-charge ratio $m/q$ with a remarkable precision of merely $\sim5$ keV. Masses of $T_z = -3/2$ fp-shell nuclides are re-determined with high accuracy, and the validity of the isospin multiplet mass equation is tested up to the heaviest isospin quartet with $A = 55$. The new masses are also used to investigate the mirror symmetry of empirical residual proton-neutron interactions.