Degrees of irreducible representations are the same for all splitting fields

Statement
Suppose $$G$$ is a finite group. Then, given any splitting field $$K$$ for $$G$$ (so the characteristic of $$K$$ does not divide the order of $$G$$) it is possible to construct a bijection between the irreducible representations of $$G$$ over $$K$$ and the irreducible representations of $$G$$ over the field of complex numbers, such that the bijection preserves the degree of a representation.

In particular, this means that the fact about::degrees of irreducible representations for a finite group are the same for all splitting fields (characteristic not dividing the group order).