(*I don't beleive I can prove  (SysPrf T (notH G))->(wInconsistent T))  So instead I prove: *)

Theorem Goedel'sIncompleteness1st :
wConsistent T ->
exists f : Formula,
~ SysPrf T f /\
~ SysPrf T (notH f) /\ (forall v : nat, ~ In v (freeVarFormula LNN f)).