
theorem Th7:
  for OAS being OAffinSpace holds for o,a,b,a9,b9 being Element
 of OAS st not o,a,b are_collinear & a,o // o,a9 &
  o,b,b9 are_collinear & a,b '||' a9,b9
  holds b,o // o,b9 & a,b // b9,a9
proof
  let OAS be OAffinSpace;
  let o,a,b,a9,b9 be Element of OAS such that
A1: not o,a,b are_collinear and
A2: a,o // o,a9 and
A3: o,b,b9 are_collinear and
A4: a,b '||' a9,b9;
  Mid a,o,a9 & a,b '||' b9,a9 by A2,A4,DIRAF:22,def 3;
  then Mid b,o,b9 by A1,A3,PASCH:6;
  hence b,o // o,b9 by DIRAF:def 3;
  hence thesis by A1,A2,A4,PASCH:12;
end;
