if and only if vs if only

if and only if

conj
  • Is equivalent to; implies and is implied by; is true and false in the same cases as. 

  • If, with added intensity 

if only

conj
  • Used other than figuratively or idiomatically: see if, only. 

  • I wish that; signifies a wish or desire for the present or the future. 

  • I wish that; signifies a regret about an action in the past. 

  • Even if for no other reason than; only just. 

How often have the words if and only if and if only occurred in a corpus of books? (source: Google Ngram Viewer )