I Covariant Derivative: 2nd Diff - My Question

Kisok
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On p158 of General Relativity written by Hobson et al., there is second differentiation of the covariant derivative. However hard I tried to understand why the first equality for the second differentiation holds, I could not. I would be very appreciated if someone help me why it should be.
My question is shown in Summary section. Please see the attached file.
 

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Well, what is this ##\nabla_cT_{ba}## equal to?
 
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