How does Boyle's law apply in crushing a heated soda can when plunged into ice water?

When a soda can is heated with some water and then plunged into ice water, Charles law says that as temperature drops, volume will drop, and then the atmospheric pressure outside the can will crush it in. But how does Boyle's law (P1V1=P2V2) relate to all of this? It seems that, by Boyle, law, pressure in the can should increase as the volume decreases, as they are indirectly proportional? I dont see how Boyle's law relates to this.

Higher pressures exerted on the outside of the can will press in upon the can ~> lower volume

Boyle's law says pressure and volume vary inversely as long as the temperature remains constant. here, the temperature doesn't remain constant, so perhaps it doesn't apply.

as the can is heated, the air inside it becomes less dense than the air outside of the can. as it is put into the ice water, something happens.. sorry, i just learned about this and already forgot.. its something like that

it crushes

hey