Combo of the Day: Their life total is 10 and they’ve milled a very large number of cards (assuming EDH)
Edit: Yes, this does work. The Sphinx changing life totals counts as loss of life (or life gain).
“2/1/2009 For a player’s life total to become 10, what actually happens is that the player gains or loses the appropriate amount of life. For example, if the targeted player’s life total is 4 when this ability resolves, it will cause that player to gain 6 life; alternately, if the targeted player’s life total is 17 when this ability resolves, it will cause that player to lose 7 life. Other cards that interact with life gain or life loss will interact with this effect accordingly.”
Are you suggesting the Hair Loop, which has been passed down by the Armstrong family for generations, which has survived countless battles and remained perfectly coiffed, is not a testament to the ELEGANCE and STRENGTH of the Armstrong legacy?!