  Observations of the high degree of isotropy of the cosmic microwave
background are commonly believed to indicate that the Universe is `almost'
Friedmann-Lemaitre-Robertson-Walker (at least since the time of last
scattering). Theoretical support for this belief comes from the so-called
Ehlers-Geren-Sachs Theorem. We show that a generalization of this theorem rules
out any strong magnetic fields in the Universe. Our theoretical result is
model-independent and includes the case of inhomogeneous magnetic fields,
complementing previous results. We thus prove that cosmic microwave background
observations severely constrain all types of primordial and protogalactic
magnetic fields in the universe.
