The wikipedia on the SIA points out that it is not an assumption, but a theorem or corollary. You have simply shown this fact again. Bostrom probably first named it an assumption, but it is neither an axiom or an assumption. You can derive it from these assumptions:
I am a random sample
I may never have been born
The pdf for the number of humans is idependent of the pdf for my birth order number
The wikipedia on the SIA points out that it is not an assumption, but a theorem or corollary. You have simply shown this fact again. Bostrom probably first named it an assumption, but it is neither an axiom or an assumption. You can derive it from these assumptions:
I am a random sample
I may never have been born
The pdf for the number of humans is idependent of the pdf for my birth order number