Hubble’s Law says: Velocity (v) = H₀ × Distance (D)

Now, we also know: Redshift (z) relates to velocity & Distance relates to redshift

So in a way, we can say:

v ∝ z (at low redshift: v ≈ c × z)

z ↔ D (via cosmological model

Therefore, v ↔ D (which is Hubble’s Law)

That gives us a transitive chain: v ↔ z ↔ D

So the third element in the transitive view is redshift (z). It's the bridge between recession velocity and distance.

But here’s the caveat, this holds nicely only at low redshift. At higher redshift, the relationships become nonlinear, and full cosmological models are needed in order to relate these quantities properly.

Still, thinking of redshift as the "middle term" is a very helpful intuition.