It is shown that the Bogoliubov-de Gennes equations pair the electrons in
states which are linear combinations of the normal states. Accordingly, the
BCS-like reduction procedure is required to choose a correct pairing. For a
homogeneous system, we point out that the kernel of the self-consistency
equation derived from the Bogoliubov-de Gennes equations needs to be
constrained by the BCS pairing condition. In the presence of ordinary
impurities, on the other hand, the Bogoliubov-de Gennes equations should be
supplemented by Anderson's pairing condition to obtain the correct vacuum state
by the corresponding unitary transformation. This results in localization
correction to the phonon-mediated interaction.