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He's Commander in Chief of the military.
[Edit: I got my info from Designated Survivor which didn't go into that detail @Thrustvector ]
[Edit 2: Hang on, maybe it did. Something to do with National Guard in S1?]
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Ha, the best sources! (Not like loads of my knowledge comes from The West Wing, no sirree...)
My take on that letter is it's just a reminder to the military that whatever crazy shit Trump may try and pull (and he's clearly more than a little deluded/desperate), their oath is to the constitution rather than to anything else. TBF the heads of the professional military (as opposed to whatever bootlicker Trump installs as acting SecDef) are usually pretty clear on that.
Also, I think as Biden is now President Elect, I think they'd have the power to veto a command from a mentally unstable exiting president SURELY