How to derive Bias of PCA estimator

Given the OLS (ordinary least squares) estimator
$$
Y=XB+e
$$
The PC regression estimator can be given as:
$$
B_PCR=T_r(T’_rX’XT_r)^{-1}T_r’X’Y=T_r Delta_r^{-1}T_r’X’Y
$$
where $T$ are the eigenvectors and $Delta$ the eigenvalues of X’X

The bias (compared to OLS) is given as
$$
[T_r T’_r-I_p]B=-T_{p-r}T’_{p-r}B
$$
How did they get to this result? Can someone please give/point me to a complete derivation as I really need to understand this result.