On Halmos' proof that "there is no universe"
You are right that the appeal to $B\in A$ in the bolded part of your quote is not necessary for the conclusion it's trying to draw.
I'd chalk it up to sloppy editing and move on.
You are right that the appeal to $B\in A$ in the bolded part of your quote is not necessary for the conclusion it's trying to draw.
I'd chalk it up to sloppy editing and move on.