I have in one book little proof to create.
We know that tuple can be expressed as $(a,b) = \{\{a\},\{a,b\}\}$
and I have too prove that:
$ a = c \ \land b = d \implies (a,b) = (c,d) $
I know this proof is very trivial but I'm a little too unexperienced in proofs so i want to ask if this proof I created is valid enought?
$a=c\ \land b=d \implies a=c=x\ \land b=d=y \implies \{\{x\},\{x,y\}\} = \{\{a\}\{a,b\}\} = \{\{c\},\{c,d\}\} \implies (a,b) = (c,d) $
Or is there any more basic proof?