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 /\ B is everywhere_dense
let A, B be Subset of X; :: thesis: ( A is everywhere_dense & B is everywhere_dense implies A /\ B is everywhere_dense )
assume ( A is everywhere_dense & B is everywhere_dense ) ; :: thesis: A /\ B is everywhere_dense
then ( A ` is nowhere_dense & B ` is nowhere_dense ) by Th39;
then ( (A `) \/ (B `) = (A /\ B) ` & (A `) \/ (B `) is nowhere_dense ) by TOPS_1:53, XBOOLE_1:54;
hence A /\ B is everywhere_dense by Th39; :: thesis: verum