 Thus, in particular, for any property \(F,\) by GSA and Nec we have that, necessarily, Adams has \(F\) only if he exists: \(\Box(\sfF\sfa \to \sfE!\sfa)\). The problem here is that Adams (reasonably) considers identity to be a relation; identity statements are thus simply a variety of atomic formula and, hence, it is also an instance of GSA that Adams is self-identical only if he exists, \(\sfa=\sfa \to \sfE!\sfa\). As Adams accepts the usual  laws of identity Id1 and Id2, we appear to have the following simple argument to Adams’ necessary existence: