Let $\xi^m$ and $\eta^n$ be vector bundles over a paracompact base space. Where can I find a reference to the Steifel-Whitney classes of the tensor product $\xi^m \otimes \eta^n$ being computed as follows?

There is a universal formula of the form$$w(\xi^m \otimes \eta^n) = p_{m, n} (w_1(\xi^m), \dots, w_m(\xi^m), w_1(\eta^n), \dots, w_n(\eta^n)),$$where the polynomial $p_{m, n}$ in $m + n$ variables can be characterized as follows. If $\sigma_1, \dots, \sigma_m$ are the elementary symmetric functions of indeterminates $t_1, \dots, t_m$, and if $\sigma_1', \dots, \sigma_n'$ are the elementary symmetric functions of $t_1', \dots, t_n'$, then$$p_{m, n}(\sigma_1, \dots, \sigma_m, \sigma_1', \dots, \sigma_n') = \prod_{i = 1}^n \prod_{j = 1}^n (1 + t_i + t_j').$$