let X be non empty TopSpace; :: thesis: for A, B being Subset of X st A is everywhere_dense & B is everywhere_dense holds
A meets B
let A, B be Subset of X; :: thesis: ( A is everywhere_dense & B is everywhere_dense implies A meets B )
assume ( A is everywhere_dense & B is everywhere_dense ) ; :: thesis: A meets B
then A /\ B <> {} by TOPS_3:34, TOPS_3:44;
hence A meets B by XBOOLE_0:def 7; :: thesis: verum