theorem Th23:
  p is valid implies All(x,p) is valid
proof
A1: p => ((All(x,p) => All(x,p)) => p) is valid;
  not x in still_not-bound_in All(x,p) by Th5;
  then
A2: not x in still_not-bound_in All(x,p) => All(x,p) by Th7;
  assume p is valid;
  then (All(x,p) => All(x,p)) => p is valid by A1,CQC_THE1:65;
  then (All(x,p) => All(x,p)) => All(x,p) is valid by A2,CQC_THE1:67;
  hence thesis by CQC_THE1:65;
end;
