theorem Th45:
  All(x,'not' 'not' p) => All(x,p) is valid & All(x,p) => All(x,
  'not' 'not' p) is valid
proof
  All(x,'not' 'not' p => p) is valid & All(x,p => 'not' 'not' p) is valid
  by Th23;
  hence thesis by Th31;
end;
