Crushing a Two Liter Bottle With No Hands

My daughters recently dug through their book of 101 science experiments and bookmarked several they wanted to do.  Here's the first one they picked out.  The goal is to crush a two liter bottle without using hands or tongs of any kind.

To do so, start with an empty two liter bottle and pour a cup or so of hot water in it.  Seal the bottle and lay it down in a pan/bowl.

Next pour ice water in the pan.  

Let the bottle cool for a bit and then stand it up, taking a close look at the sides of the bottle.

See how the sides have started to crush in?  What's going on here?  When warm water is poured inside, it warms the air and the air expands.  Once sealed, no air can enter or escape.  When the bottle is placed in cold ice water, the temperature of the air inside decreases and the pressure of the air decreases.  At this point, the air pressure outside the bottle is greater than the air pressure inside the bottle.  Thus the sides cave in!  And that's how you crush a two liter bottle without using your hands!