theorem
  MDist a,b & a,b // c,d implies MDist c,d
proof
  assume that
A1: MDist a,b and
A2: a,b // c,d;
A3: a,b // b,a by A1;
A4: c,d // a,b by A2,Th3;
  then d,c // b,a by Th7;
  then d,c // a,b by A3,Def1;
  then c,d // d,c by A4,Def1;
  then c <> d implies thesis;
  hence thesis by A1,A2,Def1;
end;
