Given that B is a symmetric matrix how can I show that if B can be diagonalized then there exists an orthonormal basis of eigenvectors of B?

Question

Suppose that $B \in R^{n \times n}$ is a symmetric matrix.

How do I prove that if $B$ can be diagonalized, then there must be an orthonormal basis ($v_1,v_2, \dots, v_n$) of eigenvectors of $B$?

This is different than the question tagged as duplicate because I am asking for a proof for that there must be an orthonormal basis rather than just proving vectors are orthogonal.