Does using std::move on pair.first invalidate pair.second?

I have the following code in my project at the moment :

std::vector<int> vectorOfFirsts;
std::set<double> setOfSeconds;
std::list<std::pair<int,double>> cachedList;
// do something to fill the list 
for (const auto& pair : cachedList)
{
   vectorOfFirsts.push_back(pair.first);
   setOfSeconds.insert(pair.second);
}

This list will be very big, and is only necessary for filling the vector and the set (i.e. its content can be invalidated). My question now is, if the following optimization is a good idea:

 for (const auto& pair : cachedList)
 {
       vectorOfFirsts.push_back(std::move(pair.first));
       setOfSeconds.insert(std::move(pair.second));
 }

Will calling std::move on pair.first somehow invalidate pair.second? And will this code provide any speedup for the loop? I know that it would probably be a good idea to fill the vector/set instead of the list, but the list is filled via some legacy code I have no control over / no time to dig in.