Let C and D be Reedy categories (or just direct categories for simplicity) and let (M,\wedge be a monoidal model category. I'm trying to show that the exterior product
\wedge\colon M^C\times M^D \to M^{C\times D}, (X,Y)\mapsto X_c\wedge Y_d
is left Quillen (In the case of the direct categories i am interested in the projective model structure). Is there some reference which i can look?