Confusion on repeated index for Einstein Summation

The rule for Einstein notation is that the same dummy index cannot be repeated twice. However suppose I want to compute Christoeffel symbols:
$$
Gamma^{alpha}_{betagamma} = frac{1}{2}g^{alphasigma}(partial_beta g_{gammasigma}+partial_{gamma}g_{sigmabeta}-partial_{sigma}g_{betagamma})
$$

Now if my metric is diagonal, then only the terms $alpha = sigma$ survive, hence we have:
$$
Gamma^{alpha}_{betagamma} = frac{1}{2}g^{alphaalpha}(partial_beta g_{gammaalpha}+partial_{gamma}g_{alphabeta}-partial_{alpha}g_{betagamma})
$$

Of course now the problem is that the index $alpha$ is repeated three times. However, it makes perfect sense to me when I do the computation. Is there some exception to the "not repeated twice" rule?