In Tao's Analyis I, one motivation for introducing the axiom of replacement is that one cannot obtain the set $\{4,6,10\}$ from $\{3,5,9\}$. While I intuitively understand this, is there a somewhat rigourous proof to show that the above cannot be achieved using the axioms introduced so far in his book: extensionality, empty set, pair set, pairwise union, specification (and perhaps axiom of infinity to make sense of the given sets)?
I include a snapshot of quoted example:
