Use Rules of Inference and Equivalence Laws to prove that the following argument is a contradiction.

$1)$ ~$(($~x$1$ v x$2)^$ x$2)$

$2)($x$1<->$ x$1)$

$3)$ ~$($~$($ x$2^($x$3$ v ~x$2))$

conclusion $($~x$1<->$ x$1)$