theorem
  not x in still_not-bound_in p & p '&' All(x,q) is valid implies All(x,
  p '&' q ) is valid
proof
  assume that
A1: not x in still_not-bound_in p and
A2: p '&' All(x,q) is valid;
  (p '&' All(x,q)) => All(x,p '&' q) is valid by A1,Th66;
  hence thesis by A2,CQC_THE1:65;
end;
