nctu writes:
> how to prove ?
>
> (a,b)=(c,d) <==> a=c, b=d
It's obvious that if a=c and b=d then (a,b)=(c,d). For the other direction, you can start by proving that if {x,y}={x,z} then y=z. Now suppose (a,b)=(c,d), that is, {{a},{a,b}}={{c},{c,d}}. Either {a}={c} or {a}={c,d}, both of which imply that c=a. So we have {{c},{c,b}}={{c},{c,d}}, and therefore {c,b}={c,d}, and therefore b=d.
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