What is de nada mean?

The English equivalents of the Portuguese and Spanish Words 'te' and 'nada' are the following: 'te', which is the direct object form of the second person pronoun, is 'you'; and 'nada', which is the third person form of the verb 'nadar', is '[he/she/it] swims'. But the verb doesn't take a direct object in Portuguese, or in Spanish. And so the phrase instead must be 'de nada', which may be an answer to being thanked. For it's the equivalent of the English 'You're welcome', 'No problem', 'It's no problem', or 'Don't mention it'.