  We introduce an all-versus-nothing proof of impossibility of
Einstein-Podolsky-Rosen's local elements of reality for two photons entangled
both in polarization and path degrees of freedom, which leads to a Bell's
inequality where the classical bound is 8 and the quantum prediction is 16. A
simple estimation of the detection efficiency required to close the detection
loophole using this proof gives eta > 0.69. This efficiency is lower than that
required for previous proposals.
