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Aladdin wished that genie would make him into a prince.
Not to make him look like a prince
Not to trick people into making them think he was a prince.
He was to be a prince.
... and then later we find out that all along, this entire time, his Father is none other than THE KING OF THIEVES.
When Aladdin met Genie, Genie's introductory song starts with the line, verbatim:
"Well Ali Baba had them forty thieves..."
That's literally the group Aladdin's father was LEADING, all along, at the time.
And what's Aladdin's name as a prince?
Ali ~~a~~Bab~~w~~a.
Clearly just a coincidence.
...
or maybe it could have just been magic ๐