Relationship between Bessel function of the first kind and the second kind of integer orders

Question

I noticed, numerically, the following relationship between Bessel function of the first kind $J_\nu(z)$ and Bessel function of the second kind $Y_\nu(z)$ for $\nu \in \mathbb{Z}$ and $z > 0$

$$2J_\nu(-z) = \mathrm{Im}[Y_\nu(-z)]$$

For example, for $\nu = 0,1,2$, I plotted the left and right expressions in Mathematica with the following code

For[n = 0, n < 3, n++, 
 Plot[{2*BesselJ[n, -x], Im[BesselY[n, -x]]}, {x, 0, 5}, 
   PlotLegends -> "Expressions"] // Print]

plots

I looked up the properties of Bessel functions on Wikipedia but couldn't see anything that directly demonstrates this relationship. Could anyone help prove it/disprove it? I'm not a mathematician, so apologies if this is a trivial question.