  We demonstrate that 3+1-dimensional quantum electrodynamics with fermionic
charges, fermionic monopoles, and fermionic dyons arises at the edge of a
4+1-dimensional gapped state with short-range entanglement. This state cannot
be adiabatically connected to a product state, even in the absence of any
symmetry. This provides independent evidence for the obstruction found by
arXiv:1306.3238 to a 3+1-dimensional short-distance completion of all-fermion
electrodynamics. The non-triviality of the bulk is demonstrated by a novel
fermion number anomaly.
