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.