Mpls beginner question

I am pretty new to mpls... I have a question on label assignment.

The ldp generates a label for each prefix it knows. It also sends this label to its neighbor. Lets say this router as R1. The neighbor (R2) would have also assigned some label to the same prefix as it would have learned the same prefix through igp.

So, when R1 and R2 exchange their labels, will R1 assign R2's label as outgoing label and its own generated label as local label ??

Is my understanding correct ??