1
general::
Phrase(s): to the contrary [and] on the contrary
as the opposite of what has been stated; contrary to what has been stated. • The brown horse didn’t beat the black horse. To the contrary, the black one won. • Among spiders, the male is not the larger one. On the contrary, the female is larger.
McGrawhill's American Idioms And Phrasal Verbs
2
general::
To the opposite effect, in denial, as in No matter what they say to the contrary, I am positive that he was present. This idiom was first recorded in 1512. Also see ON THE CONTRARY.
American Heritage Idioms