Why is a Hydrogen bomb called a hydrogen bomb?

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I know that a teller-ulam device uses lithium deuteride as its nuclear fuel.

I know very little about chemistry, but why is a hydrogen bomb called a hydrogen bomb, if its nuclear fuel is lithium deuteride?

Is it the hydrogen atom in the lithium deuteride that creates the fusion process?
 
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Lithium bomb sounds sissified.

Really though it's the tritium and deuterium that undergoes fusion.
 
Deuteride as in LiD, is hydrogen with 1 neutron and 1 proton. In the flux of the detonation, the lithium decomposes into tritium (2 for 1) in the case of lithium6, and tritium and a neutron in the case of lithium7. As I recall, lithium is 60/40 6 and 7. Or maybe I have that backwards . . .

Anyhow, the lithium deuteride is pretty much all hydrogen isotopes by the time it is consumed and 'burned' into helium.