Notre Dame Journal of Formal Logic

Negation-Free and Contradiction-Free Proof of the Steiner–Lehmus Theorem

Victor Pambuccian

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By rephrasing quantifier-free axioms as rules of derivation in sequent calculus, we show that the generalized Steiner–Lehmus theorem admits a direct proof in classical logic. This provides a partial answer to a question raised by Sylvester in 1852. We also present some comments on possible intuitionistic approaches.

Article information

Notre Dame J. Formal Logic, Volume 59, Number 1 (2018), 75-90.

Received: 22 March 2014
Accepted: 1 June 2015
First available in Project Euclid: 1 September 2017

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 03F07: Structure of proofs
Secondary: 03B30: Foundations of classical theories (including reverse mathematics) [See also 03F35] 51F05: Absolute planes

Steiner–Lehmus theorem direct proof indirect proof sequent calculus absolute geometry


Pambuccian, Victor. Negation-Free and Contradiction-Free Proof of the Steiner–Lehmus Theorem. Notre Dame J. Formal Logic 59 (2018), no. 1, 75--90. doi:10.1215/00294527-2017-0019.

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