theorem
  not x in still_not-bound_in p & Ex(x,p) is valid implies p is valid
proof
  assume that
A1: not x in still_not-bound_in p and
A2: Ex(x,p) is valid;
  Ex(x,p) => p is valid by A1,Th20;
  hence thesis by A2,CQC_THE1:65;
end;
