An inference of

natural deduction In logic and proof theory, natural deduction is a kind of proof calculus in which logical reasoning is expressed by inference rules closely related to the "natural" way of reasoning. This contrasts with Hilbert-style systems, which instead use a ...

is a normal form, according to

Dag Prawitz Dag Prawitz (born 1936, Stockholm) is a Swedish philosopher and logician. He is best known for his work on proof theory and the foundations of natural deduction. Prawitz is a member of the Norwegian Academy of Science and Letters, of the Roya ...

, if no formula occurrence is both the principal premise of an elimination rule and the conclusion of an introduction rule.

References

Logic {{Logic-stub