on the contrary

• to the contrary

on the contrary

1. (conjunctive) opposite of what had earlier been expected or assumed
   • 2013 April 9, Andrei Lankov, “Stay Cool. Call North Korea’s Bluff.”, in New York Times‎:

     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.

• (opposite of what had earlier been assumed): au contraire, if anything, far from it
• contrariwise