two dimension STL vector thread safe?

Suppose I have a 2 dimension vector

vector< vector< int> > v

Then thread 1 operate on v[0], like

v[0].append(x)

thread 2 operate on v[1],

v[1].remove(y)

etc.

Is this operation thread safe? I suppose it is, as v[0] and v[1] are separate pointers which point to different memory? but not sure.