Since veh_id is a primary key, it is by definition already unique. It makes no sense, and has zero positive impact on performance, to include it in an index.
Indeed, the reason not to include it is in case somehow the veh_type changes in the future.
Subtypes can be attribute (column) in the supertype -- not as common, but it can be done -- but it shouldn't be part of any identifying key.
To confirm this, fill in some of the "other_columns". Then apply 3NF and BCNF rules: do all of the 'other columns' directly depend on the "whole key and nothing but the key?" With the veh_type in there, my guess is that they do not, as the veh_type is not needed for dependency.