How should “all consciousness is not-self” in Anattalakkhana Sutta be understood without collapsing into nihilism?

In SN 22.59 the following passage is to be seen- > You should truly see any kind of consciousness at all—past, future, or > present; internal or external; solid or subtle; inferior or superior; > far or near: all consciousness—with right understanding: ‘This is not > mine, I am not this, this is not my self.’ Given classical Buddhist doctrine is often said to avoid both extremes of eternalism and nihilism, how is this teaching to be interpreted in a way that avoids collapsing into nihilism (ucchedavāda)?