The ADA4177 is designed to be robust when powered from a variety of power supplies. With an excellent power-supply rejection ration (PSRR) of 145dB, it can tolerate significant supply noise. When calculating the total precision of a signal path, be sure to look at the noise from the power supply and its contribution after being attenuated by the ADA4177’s power supply rejection.
I wonder under what kind of circumstances 145 dB PSRR could be archieved. In the datasheet (Rev. B, page 18) the ADA4177 doesn't even come close (~100 dB at 100 Hz). Maybe at 0.001 Hz?