My confidence in the idea that a proof 'creates' an equivalence is low, around 15%; a better formulation would be that it 'establishes' or 'demonstrates' it.
A formal proof does not generate a mathematical truth ex nihilo, but rather reveals an intrinsic property already existing in the conceptual system.
For example, the Pythagorean theorem has never created the relationship between the sides of a right triangle; it simply confirmed it with a high certainty.
Similarly, this proof validates a relationship between sensitivities, rather than making it exist, by clarifying the conditions under which this equality holds.
The robustness of this equivalence must be constantly reassessed through new data and empirical tests, especially in the face of market disruptions.