let T be TopStruct ; :: thesis: for F, G being Subset-Family of T st F c= G & G is open holds
F is open
let F, G be Subset-Family of T; :: thesis: ( F c= G & G is open implies F is open )
assume A1: ( F c= G & G is open ) ; :: thesis: F is open
let P be Subset of T; :: according to TOPS_2:def 1 :: thesis: ( P in F implies P is open )
assume P in F ; :: thesis: P is open
hence P is open by A1, Def1; :: thesis: verum