Metamath Proof Explorer


Theorem frege59a

Description: A kind of Aristotelian inference. Namely Felapton or Fesapo. Proposition 59 of Frege1879 p. 51.

Note: in the Bauer-Meenfelberg translation published in van Heijenoort's collectionFrom Frege to Goedel, this proof has the frege12 incorrectly referenced where frege30 is in the original. (Contributed by RP, 17-Apr-2020) (Proof modification is discouraged.)

Ref Expression
Assertion frege59a if- φ ψ θ ¬ if- φ χ τ ¬ ψ χ θ τ

Proof

Step Hyp Ref Expression
1 frege58acor ψ χ θ τ if- φ ψ θ if- φ χ τ
2 frege30 ψ χ θ τ if- φ ψ θ if- φ χ τ if- φ ψ θ ¬ if- φ χ τ ¬ ψ χ θ τ
3 1 2 ax-mp if- φ ψ θ ¬ if- φ χ τ ¬ ψ χ θ τ