 Given these axioms, it is possible to form conservative extensions of the deduction theorem that permit the use of additional connectives.These extensions are called conservative because if a formula φ involving new connectives is rewritten as a logically equivalent formula θ involving only negation, implication, and universal quantification, then φ is derivable in the extended system if and only if θ is derivable in the original system.When fully extended, a Hilbert-style system will resemble more closely a system of natural deduction.