I suggest to add this, which I keep adding to my org-user-entities:

(("frac23" "\\frac23" t "⅔" "2/3" "⅔" "⅔")
 ("over" "\\over" t "/" "/" "/" "/")
 ("iff" "\\iff" t "&hArr;" "<=>" "<=>" "⇔")
 ("implies" "\\implies" t "&rArr;" "=>" "=>" "⇒"))

The two first just allow to type simple fractions more readably, the two 
last add semantic variants to the already existing Rightarrow and 
Rightleftarrow.

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