let T be TopStruct ; :: thesis: for F, G being Subset-Family of T st F is open holds
F /\ G is open
let F, G be Subset-Family of T; :: thesis: ( F is open implies F /\ G is open )
assume A1: F is open ; :: thesis: F /\ G is open
let P be Subset of T; :: according to TOPS_2:def 1 :: thesis: ( P in F /\ G implies P is open )
assume P in F /\ G ; :: thesis: P is open
then P in F by XBOOLE_0:def 4;
hence P is open by A1; :: thesis: verum