> Note that if a system is inconsistent then everything is provable, thus if a system is consistent there must be a proposition which cannot be proved. ¬ ∀ (P

> Note that if a system is inconsistent then everything is provable, thus if a system is consistent there must be a proposition which cannot be proved. ¬ ∀ (P Q : Prop), (P → Q) → (¬P → ¬Q)