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e, z, mu are vectors of size N

I need to show that E(e|z+mu) = E(e|mu) or at least E(e|z+mu) converges in probability to E(e|mu) as N goes to infinity, under the assumption that Z is not correlated with e.

My guess is that to get this result I also need z to be orthogonal to mu, that is z'mu=0

I tryed using the law of iterated expectations... but my bieg problem is that I'm not sure how to handle the condictioning on the sum of z and mu.... I would realy appriciate any help !!!

Regards