theorem Th23: :: GLIB_014:23

for S being GraphUnionSet
for G being GraphUnion of S holds
( ( S is loopless implies G is loopless ) & ( G is loopless implies S is loopless ) & ( S is edgeless implies G is edgeless ) & ( G is edgeless implies S is edgeless ) & ( S is loopfull implies G is loopfull ) )