be no/nobody's fool

be no fool

To be worldly and difficult to trick or deceive. Your teacher is no fool—she'll never believe that your homework blew away on your walk home from school.
See also: fool, no

be no (or nobody's) fool

be a shrewd or prudent person.
See also: fool, no

be ˌno/ˌnobody’s ˈfool

be a clever person who cannot easily be tricked or cheated by anyone: You won’t be able to cheat her — she’s nobody’s fool.Don’t underestimate him. He’s no fool.
See also: fool, no