Have you ever seen a guitar "snake" cable? It's for people with lots of connections they need to make who don't want a ton of wires everywhere. I kind of think of the brachial plexus this way. The purple input always leads to the purple output, and even though it's all jumbled together in the black part, the colors never mix. So even though the axillary nerve gets bundled with everything else in the posterior cord, it's still just the fibers from C6 and C7 spinal nerve roots (analogy: the purple and yellow cables) that end up being the axillary nerve.
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