Antonyms for the phrase "give credence to" include "discredit", "disprove", "reject", "contradict", "oppose" and "refute". These words indicate a rejection of the validity of a certain idea, claim or belief. "Discredit" and "disprove" refer to showing evidence that discredits or invalidates a claim, while "reject" and "oppose" imply an outright refusal to accept or support the idea. "Contradict" and "refute" involve providing evidence or arguments that directly oppose the validity of the claim. These antonyms are useful in communicating a strong disagreement with a statement, theory, or belief that one may consider to be false or misleading.