theorem Th14: :: CARD_FIL:14

for X being non empty set
for Z being Subset of X
for F being Filter of X st ( for Y1 being Subset of X st Y1 in F holds
Y1 meets Z ) holds
( Z in Extend_Filter (F,Z) & Extend_Filter (F,Z) is Filter of X & F c= Extend_Filter (F,Z) )