clojure and ^:dynamic

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I tried to understand dynamic variables and binding function so I tried this (clojure 1.3):

user=> (defn f [] 
           (def ^:dynamic x 5) 
           (defn g [] (println x)) 
           (defn h [] (binding [x 3] (g))) 
           (h))
#'user/f
user=> (f)     
5
nil

Confused, I tried this somewhat simpler code:

user=> (def ^:dynamic y 5)
#'user/y
user=> (defn g [] (println y))
#'user/g
user=> (defn h [] (binding [y 3] (g)))
#'user/h
user=> (h)
3
nil

What is the difference between the two pieces of code? Why does the second example work but the first does not?

Hint: I just realized that the following works (still don't fully understand why):

user=> (def ^:dynamic y 5)
#'user/y
user=> (defn f [] (defn g [] (println y)) (defn h [] (binding [y 3] (g))) (h))
#'user/f
user=> (f)
3
nil
user=> 
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