if we are to prove
X-(X-A) = A,
what we normally do is for an arbitrary x suppose ,
x E X-(X-A)
--> x E A
x E A
---> x E X-(X-A)
this tells us X-(X-A) = A,
its perfect and theres no wrong with it.
but my question is what happens if I use biconditional statement as
x E X-(X-A) <---> x E X AND x ~E X -A
<---> some proof here
<---> x E A
then we dont want to split it into two parts as did earlier.
but why dont we normally prove like this???