theorem Th6: :: SPRECT_1:6

for T being non empty TopSpace
for A being non empty Subset of T
for B1, B2, S being Subset of T st B1 is_a_component_of A & B2 is_a_component_of A & S is_a_component_of A & B1 \/ B2 = A & not S = B1 holds
S = B2