Metamath Proof Explorer

Theorem frege23

Description: Syllogism followed by rotation of three antecedents. Proposition 23 of Frege1879 p. 42. (Contributed by RP, 24-Dec-2019) (Proof modification is discouraged.)

Ref Expression
Assertion frege23 ⊢ φ → ψ → χ → θ → τ → φ → ψ → χ → τ → θ

Proof

Step Hyp Ref Expression
1 frege18 ⊢ φ → ψ → χ → θ → τ → φ → ψ → τ → χ → θ
2 frege22 ⊢ φ → ψ → χ → θ → τ → φ → ψ → τ → χ → θ → φ → ψ → χ → θ → τ → φ → ψ → χ → τ → θ
3 1 2 ax-mp ⊢ φ → ψ → χ → θ → τ → φ → ψ → χ → τ → θ