Re: Every set x equinumerous with a set y disjoint from x?

["Rupert"]

MoeBlee wrote:
> For ZC (Z set theory with the axiom of choice), I'm pretty sure I see
> how to prove:
>
> AxEy(x equinumerous with y & x/\y = 0)
>
> where '/\' stands for binary intersection.
>
> But can this be proven without the axiom of choice? If so, how to do
> it?
> 

Yes, consider x X {x}.

> MoeBlee