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This is false because in phase changes heat can be removed but the temperature will not change. If you look at a heating curve, you'll see that temperature stays constant during a phase change despite the change in heat. i.e. When ice is in the process of melting into water (phase change), heat can be added or removed but the temperature will still remain at 0 degrees Celcius.
The first part of the statement, that removing heat from a system will be exothermic is true because heat is leaving the system. However as said before phase changes play a role in not changing temperature because heat can be added to go from one phase to the next but not change the temperature in any way.
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