A1: rng (R | X) c= rng R by RELAT_1:70;
let r be Real; :: according to PARTFUN3:def 1 :: thesis: ( not r in rng (R | X) or not r <= 0 )
assume r in rng (R | X) ; :: thesis: not r <= 0
hence not r <= 0 by A1, PARTFUN3:def 1; :: thesis: verum