`vi` command doesn't open newly installed Vim 7.4 on OS X

`vi` command doesn't open newly installed Vim 7.4 on OS X

I just installed Vim 7.4 on my MacBook using Homebrew. When I enter vim on
the command line, it successfully enters Vim 7.4, but when I use vi I
still get the old 7.3.
To install Vim 7.4 I used this command:
brew install vim --override-system-vi
When I do which:
$ which vi
/usr/local/bin/vi
When I execute this path in my shell /usr/local/bin/vi it does open 7.4.
So I thought it might be an alias, but alias vi didn't find anything.
I'm quite puzzled by this and I have no idea why this happens. Does anyone
know why this might be happening and how to fix it? I could of course make
an alias of vi to vim but I wonder why it works the way it does right now.