Single Idea 13620

[catalogued under 5. Theory of Logic / H. Proof Systems / 3. Proof from Assumptions]

Full Idea

By repeated transformations using the Deduction Theorem, any proof from assumptions can be transformed into a fully conditionalized proof, which is then an axiomatic proof.

Gist of Idea

Proof by Assumptions can always be reduced to Proof by Axioms, using the Deduction Theorem

Source

David Bostock (Intermediate Logic [1997], 5.6)

Book Reference

Bostock,David: 'Intermediate Logic' [OUP 1997], p.223


A Reaction

Since proof using assumptions is perhaps the most standard proof system (e.g. used in Lemmon, for many years the standard book at Oxford University), the Deduction Theorem is crucial for giving it solid foundations.