defpred S_{1}[ Element of M] means $1 is_between p,r;

{ q where q is Element of M : S_{1}[q] } c= the carrier of M
from FRAENKEL:sch 10();

hence { q where q is Element of M : q is_between p,r } is Subset of M ; :: thesis: verum

{ q where q is Element of M : S

hence { q where q is Element of M : q is_between p,r } is Subset of M ; :: thesis: verum