theorem Th13:
  p<>q implies ex r st not p,q // p,r
proof
  consider a,b,c such that
A1: not a,b // a,c by Def1;
  assume p<>q;
  then not p,q // p,a or not p,q // p,b or not p,q // p,c by A1,Th12;
  hence thesis;
end;
