$\displaystyle E[\hat{\beta}_0] = {\beta}_0$

in the model $\displaystyle Y_i = {\beta}_0 + B_1X_i + u_i$

$\displaystyle \hat{\beta}_0 = \bar{y} + \hat{\beta}_1\bar{x}$

if I take the expectation of both sides I get

$\displaystyle E(\hat{\beta_0}) = \mu_y + \hat{\beta}_1 \mu_x$

why is this equal to $\displaystyle \hat{\beta}_0$?