Self-duality implies Yang-Mills equations ($D_{A}F=0,\ast F=\pm F⟹D_A\ast F=0$)

Both the self-dual Yang-Mills equations and the Anti-self-dual Yang-Mills equations imply the second-order Yang-Mills equations because the Bianchi identity holds for every principal connection. Finite action is additionally required to call the solution a Yang-Mills instanton; the implication itself is a local differential identity.