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.
The American Heritage® Idioms Dictionary Copyright © 2002, 2001, 1995 by Houghton Mifflin Harcourt Publishing Company. Published by Houghton Mifflin Harcourt Publishing Company.