reserve r,s,t,u for Real;
reserve V for RealLinearSpace,
  v,w for Point of V;
reserve x1,x2,x3,x4,y1,y2 for Element of V;

theorem
 for V being non trivial RealLinearSpace, L being non trivial line of V
  ex p,q being Point of V st p <> q & L = Line(p,q)
proof let V be non trivial RealLinearSpace, L be non trivial line of V;
  consider p,q being object such that
A1: p in L & q in L and
A2: p <> q by ZFMISC_1:def 10;
  reconsider p,q as Point of V by A1;
 take p,q;
 thus p <> q by A2;
  ex x1,x2 being Element of V st L = Line(x1,x2) by Def15;
 hence L = Line(p,q) by A2,Th75,A1;
end;
