  In this paper, we show that the Character Triple Conjecture holds for all
finite groups once assumed for all quasi-simple groups. This answers the
question on the existence of a self-reducing form of Dade's conjecture, a
problem that was long investigated by Dade in the 1990s. Our result shows that
this role is played by the Character Triple Conjecture, recently introduced by
Sp\"ath, that we present here in a general form free of all previously imposed
restrictions.
