theorem
  (ex a,b st a<>b & for c holds a,b '||' a,c) implies for p,q,r,s holds
  p,q '||' r,s
proof
  assume ex a,b st a<>b & for c holds a,b '||' a,c;
  then consider a,b such that
A1: a<>b and
A2: for c holds a,b '||' a,c;
  let p,q,r,s;
  a,b '||' a,r & a,b '||' a,s by A2;
  then
A3: a,b '||' r,s by Th35;
  a,b '||' a,p & a,b '||' a,q by A2;
  then a,b '||' p,q by Th35;
  hence thesis by A1,A3,Def11;
end;
