theorem Th41: :: BVFUNC11:41

for Y being non empty set
for a being Function of Y,BOOLEAN
for G being Subset of (PARTITIONS Y)
for A, B being a_partition of Y st G is independent holds
'not' (All ((Ex (a,A,G)),B,G)) '<' All (('not' (All (a,B,G))),A,G)