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 Th24:
  A is being_line & a in A & b in A & a<>b & LIN a,b,x implies x in A
proof
  assume that
A1: A is being_line and
A2: a in A and
A3: b in A and
A4: a<>b and
A5: LIN a,b,x;
  A=Line(a,b) by A1,A2,A3,A4,Lm6;
  hence thesis by A5,Def2;
end;
