reserve AS for AffinSpace;
reserve a,a9,b,b9,c,d,o,p,q,r,s,x,y,z,t,u,w for Element of AS;
reserve A,C,D,K for Subset of AS;

theorem Th19:
  A is being_line implies ex b st a<>b & b in A
proof
  assume A is being_line;
  then consider p,q such that
A1: p in A and
A2: q in A and
A3: p<>q by Th18;
  a=p implies a<>q & q in A by A2,A3;
  hence thesis by A1;
end;
