How I can subtract a blurry alpha channel from another alpha channel in the compositor?
First alpha channel
Second alpha channel
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You need nothing more then a Mix node set to Subtract with a factor of one.
To replicate your bottom image, plug your first image in to the first socket on the mix node, and the blurry image into the second socket.
*) When the substract operation is used,make sure to mark the "clamp" checkbox to avoid negative values in the result.