theorem
  not x in still_not-bound_in p implies ( p 'or' All(x,q) is valid iff
  All(x,p 'or' q) is valid)
proof
  assume not x in still_not-bound_in p;
  then (p 'or' All(x,q)) <=> All(x,p 'or' q) is valid by Th69;
  hence thesis by Lm15;
end;
