for a fact vs i.e.

for a fact

adv
  • Used other than figuratively or idiomatically: see for, a, fact. 

  • Without doubt. 

i.e.

adv
  • That is, namely, in other words, that is to say. 

How often have the words for a fact and i.e. occurred in a corpus of books? (source: Google Ngram Viewer )