Metamath Proof Explorer

Theorem frege20

Description: A closed form of syl8 . Proposition 20 of Frege1879 p. 40. (Contributed by RP, 24-Dec-2019) (Proof modification is discouraged.)

Ref Expression
Assertion frege20 ⊢ φ → ψ → χ → θ → θ → τ → φ → ψ → χ → τ

Proof

Step Hyp Ref Expression
1 frege19 ⊢ ψ → χ → θ → θ → τ → ψ → χ → τ
2 frege18 ⊢ ψ → χ → θ → θ → τ → ψ → χ → τ → φ → ψ → χ → θ → θ → τ → φ → ψ → χ → τ
3 1 2 ax-mp ⊢ φ → ψ → χ → θ → θ → τ → φ → ψ → χ → τ