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An inference of natural deduction is a normal form, according to Dag Prawitz, if no formula occurrence is both the principal premise of an elimination rule and the conclusion of an introduction rule.

References

1. Prawitz, Dag (2006). Natural Deduction: A Proof-Theoretic Study. Mineola, New York: Dover Publications. ISBN 9780486446554. OCLC 61296001.

v t e Normal forms in logic
Propositional logic	Negation normal form Conjunctive normal form Disjunctive normal form Algebraic normal form (Zhegalkin polynomial) Blake canonical form Canonical normal form Horn clause
Predicate logic	Skolem normal form Herbrandization Prenex normal form
Other	Beta normal form Modal clausal form Normal form (natural deduction)

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