Expectation of random variable with omitted variable bias

Question

I am given:

$y_i = \beta_0 + \beta_1range_i + \beta_2dist_i + \epsilon_i$

$E[\epsilon_i | range_i, dist_i]=0$

Then in the case where $dist_i$ is omitted:

$y_i = \beta_0 + \beta_1range_i + \eta_i$

Do we know that $E[\eta_i|range_i] =0$?

My first instinct was to try to compute $E[\beta_2dist_i + \epsilon_i|range_i]$, but I don't know if this helps me with anything.

How can I answer my question?