A1: rng (chi x,y) c= {0 ,1} by FUNCT_3:48;
{0 ,1} c= [.0 ,1.]

proof

( 1 in [.0 ,1.] & 0 in [.0 ,1.] ) by XXREAL_1:1;
hence {0 ,1} c= [.0 ,1.] by ZFMISC_1:38; :: thesis: verum

end;

hence rng (chi x,y) c= [.0 ,1.] by A1, XBOOLE_1:1; :: according to RELAT_1:def 19 :: thesis: verum