How do i make myself unavailable for facebook chat on my mobile phone?

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So with the new facebook chat, my boyfriend has noticed on his chat, that i'm always online and i have a little mobile phone next to my name, and when you click my name it says send a message to so and so's phone. But i dont want people to be able to do this, how to i disable it, so i can still go on facebook on my phone but not be online to my friends. I've tried signing out of facebook on my phone, but my boyfriend says its still there, never goes awayy? how to i get rid of this pleasee someone help?
 
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