Equation with Riemann curvature tensor

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

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