let FT be non empty RelStr ; :: thesis: for x being Point of FT holds {x} is connected
let x be Point of FT; :: thesis: {x} is connected
assume not {x} is connected ; :: thesis: contradiction
then consider P, Q being Subset of FT such that
A1: {x} = P \/ Q and
A2: P <> {} and
A3: Q <> {} and
A4: P misses Q and
( not P ^b meets Q or not P meets Q ^b ) ;
P <> Q by A2, A4;
hence contradiction by A1, A2, A3, ZFMISC_1:38; :: thesis: verum