Partial derivatives and substituitions with SymPy

Question

I have the following code where I define a composite function f(r(x,y),theta(x,y)), and I'm trying to simplify f.diff(x) assuming that I know an expression for f.diff(r):

x, y = sp.symbols("x y", real=True)
r    = sp.Function('r')(x, y)
phi  = sp.Function('phi')(x, y)
f      = sp.Function('f')(r, phi)
df_dr  = sp.Function('df_dr')(r, phi)
df_phi = sp.Function('df_phi')(r, phi)

Next, I compute the derivatives of f(r,phi) with respect to x:

f.diff(x)

And I get the following:

Derivative(phi(x, y), x)*Subs(Derivative(f(r(x, y), _xi_2), _xi_2), _xi_2, phi(x, y)) + Derivative(r(x, y), x)*Subs(Derivative(f(_xi_1, phi(x, y)), _xi_1), _xi_1, r(x, y))

My question is: how can I replace Subs(Derivative(f(_xi_1, phi(x, y)), _xi_1) by df_dr?