Degree of irreducible representation of symmetric group equals sum of degrees of irreducible representations for partitions with one box less

Statement
Suppose $$\lambda$$ is an unordered integer partition of $$n$$, Suppose $$\mu_1, \mu_2, \dots, \mu_r$$ are all the unordered integer partitions of $$n - 1$$ such that the Young diagram for $$\lambda$$ can be obtained by adding just one box to the Young diagram for $$\mu_i$$. Then, the degree of $$\lambda$$ equals the sum of the degrees of the $$\mu_i$$s.

Facts used

 * 1) uses::Pieri's rule