me@host$ sudo docker run -it ubuntu:xenial

root@container# apt update && apt install python3-pip

root@container# pip3 --version
pip 8.1.1 from /usr/lib/python3/dist-packages (python 3.5)

root@container# pip3 install --upgrade pip
Collecting pip
  Downloading pip-10.0.0-py2.py3-none-any.whl (1.3MB)
    100% |################################| 1.3MB 1.4MB/s 
Installing collected packages: pip
  Found existing installation: pip 8.1.1
    Not uninstalling pip at /usr/lib/python3/dist-packages, outside environment /usr
Successfully installed pip-10.0.0

root@container# pip --version
pip 10.0.0 from /usr/local/lib/python3.5/dist-packages/pip (python 3.5)

root@container# pip3 --version
Traceback (most recent call last):
  File "/usr/bin/pip3", line 9, in <module>
    from pip import main
ImportError: cannot import name 'main'

root@container# cat /usr/bin/pip3
#!/usr/bin/python3
# GENERATED BY DEBIAN

import sys

# Run the main entry point, similarly to how setuptools does it, but because
# we didn't install the actual entry point from setup.py, don't use the
# pkg_resources API.
from pip import main
if __name__ == '__main__':
    sys.exit(main())