on the contrary

prep_phrase

1. Opposite of what had earlier been expected or assumed; to the contrary.

   “Many persons have an idea that a habitually dark room is best for the eyes. On the contrary, it weakens them and renders them permanently unable to bear the light of the sun.”

   “Even if they managed to strike Japan, the United States or South Korea with nuclear weapons — a big if, given that they do not have a reliable delivery system — they could not save themselves from ultimate defeat. On the contrary, the use of nuclear or other terror weapons would be certain to invite overwhelming retaliation, delivering North Korea’s decision makers to a fiery oblivion.”