The relationship between enthalpy change and entropy change is governed by the Gibbs free energy equation (delta G = delta H - T delta S), and it is a fundamental thermodynamic principle that processes can have a negative enthalpy change and a positive entropy change (which makes them spontaneous at all temperatures).
The claim is a fundamental thermodynamic principle based on the definition of Gibbs free energy (delta G = delta H - T delta S). An exothermic process (negative delta H) accompanied by an increase in disorder (positive delta S) results in a negative delta G, making the process spontaneous. This is a basic textbook definition and everyday scientific fact, rendering it common knowledge that requires no citation.