Equation with Riemann curvature tensor

[paweld]

Can anyone prove the following formula:
$$R_{abf}^{\phantom{abf}e} \Gamma_{cd}^f = R_{abc}^{\phantom{abc}f} \Gamma_{fd}^e + R_{abd}^{\phantom{abd}f} \Gamma_{cf}^e$$
I found it in "General Relativity" by Wald (in slightly different notation).

 

[javierR]

If you write it out in terms of the derivatives of metric components, you should be able to manipulate the expression until you get the indices arranged as you want.