reserve a,b,s,t,u,lambda for Real,
  n for Nat;
reserve x,x1,x2,x3,y1,y2 for Element of REAL n;
reserve p1,p2,q1,q2 for Point of TOP-REAL n;

theorem :: AFF_1:32
  for A being Subset of TOP-REAL n st A is being_line holds ex p2 st p1
  <>p2 & p2 in A
proof
  let A be Subset of TOP-REAL n;
  assume A is being_line;
  then consider q1,q2 such that
A1: q1 in A and
A2: q2 in A & q1<>q2 by Th44;
  p1 = q1 implies p1<>q2 & q2 in A by A2;
  hence thesis by A1;
end;
