theorem Th53:
  L is being_line implies ex x1 st x1 <> x0 & x1 in L
proof
  assume L is being_line;
  then consider y1,y2 such that
A1: y1 in L and
A2: y2 in L & y1 <> y2 by EUCLID_4:13;
  now
    per cases;
    case
A3:   y1 = x0;
      take y2;
      thus y2 <> x0 & y2 in L by A2,A3;
    end;
    case
A4:   y1 <> x0;
      take y1;
      thus y1 <> x0 & y1 in L by A1,A4;
    end;
  end;
  hence thesis;
end;
