reserve AFV for WeakAffVect;
reserve a,b,c,d,e,f,a9,b9,c9,d9,f9,p,q,r,o,x99 for Element of AFV;

theorem Th23:
  Mid a,b,c & MDist b,b9 implies Mid a,b9,c
proof
  assume that
A1: Mid a,b,c and
A2: MDist b,b9;
A3: b,b9 // b9,b by A2;
  a,b // b,c by A1;
  then
A4: b,a // c,b by Th7;
  consider d such that
A5: b9,b // c,d by Def1;
  c,d // b9,b by A5,Th3;
  then b,b9 // c,d by A3,Def1;
  then
A6: a,b9 // b,d by A4,Def1;
  b9,c // b,d by A5,Def1;
  then a,b9 // b9,c by A6,Def1;
  hence thesis;
end;
