The phrase "crossed mind" implies a fleeting thought or idea. Antonyms for this phrase could include "dominant thought," "permanent impression," or "constant consideration." These would suggest a more focused or ingrained concept, rather than a passing notion. Other antonyms could include "ignored," "forgotten," or "dismissed," emphasizing the opposite of a thought that lingers or makes an impact. Still more antonyms might be "irrelevant," "unrelated," or "unimportant," suggesting that the opposite of a "crossed mind" idea is something that has no bearing or significance.