Although the words negate and invalidate have much in common, negate implies the destruction or canceling out of each of two things by the other.

// the arguments negate each other

Abrogate is like annul but more definitely implies a legal or official act.

// a law to abrogate trading privileges

Some common synonyms of invalidate are abrogate, annul, negate, and nullify. While all these words mean "to deprive of effective or continued existence," invalidate implies making something powerless or unacceptable by declaration of its logical or moral or legal unsoundness.

// the court invalidated the statute