reconsider F = {({} V)} as Subset-Family of V ;
take F ; :: thesis: ( not F is empty & F is convex-membered )
thus not F is empty ; :: thesis: F is convex-membered
let M be Subset of V; :: according to RLTOPSP1:def 3 :: thesis: ( M in F implies M is convex )
assume M in F ; :: thesis: M is convex
then M = {} V by TARSKI:def 1;
hence M is convex ; :: thesis: verum