We could prove P=>~P if we had earlier in our context another hypothesis Q, which is false. So proving P=>~P does not imply P is false. It means our context is

We could prove P=>~P if we had earlier in our context another hypothesis Q, which is false. So proving P=>~P does not imply P is false. It means our context is inconsistent. It could be inconsistent because of P or because of Q?