Disjointifying sets if indexed by set that doesn't admit a well-order?

Question

I have a question about the following:

I think this should say "... if $I$ finite or if there exists a well-order ..." because if $I$ is a set like this

also lets one disjointify $A_i$ with $i \in \{a,b,c,d\}$. Or am I missing something? Thanks!

Answer 1

If $I$ is finite, there is a well-ordering of $I$ in ZF. Thus, the finite case is automatically covered by ‘if there exists a wellorder relation on $I$’.