I can never figure out (because the English language is imprecise) which part of "if and only if" means which implication.
(A if and only if B) = (A <=> B), but is the following correct:
(A only if B) = (A => B)
(A if B) = (A <= B)
The trouble is, one never comes into contact with "A if B" or "A only if B" using those constructions in everyday common speech.