Why does $\vec \nabla \times \vec A = 0$ imply $\vec A = - \nabla B$ where $\vec A$ is a vector field and $B$ is a scalar field?
I see this in my Electricity and Magnetism textbooks all over the place and I just took it for granted. Is this a theorem or does it come from one?
I can verify in my head that this is valid, but I would love some context.