How to use erase-remove idiom and increment an iterator in a loop?

I want to loop through a vector and remove an item each time. I believe I should use the erase-remove idiom. I believe erase on a vector invalidates any of its iterators. If that's the case, how can I use this idiom in a while loop?

Here's a broken example:

std::vector<int> vec = { 3, 6, 7, 5 };

auto itr = vec.begin();
while (itr != vec.end())
{
    // I'll remove a different element each iteration of the loop.
    // Hard-coded "7" here for simplicity:
    auto position = std::find(vec.begin(), vec.end(), 7);

    vec.erase(position);
    ++itr;
}