as it happens vs undeniably

as it happens

adv
  • By coincidence, incidentally 

undeniably

adv
  • In an undeniable manner, or to an undeniable extent. 

  • Used as a modal adverb to assert that that the indicated statement is undeniable. 

How often have the words as it happens and undeniably occurred in a corpus of books? (source: Google Ngram Viewer )