Pravda - Hilbert's proof systems
Hilbert system in propositional logic
Hibert system in propositional logic is extremely simple: 3 axiom schemes and modus ponens.
p -> (p -> p) (p -> ((p -> p) -> p)) (p -> ((p -> p) -> p)) -> ((p -> (p -> p)) -> (p -> p)) //((p -> (p -> p)) -> (p -> p)) p -> p