Metamath Proof Explorer

Theorem frege22

Description: A closed form of com45 . Proposition 22 of Frege1879 p. 41. (Contributed by RP, 24-Dec-2019) (Proof modification is discouraged.)

Ref Expression
Assertion frege22 ⊢ φ → ψ → χ → θ → τ → η → φ → ψ → χ → τ → θ → η

Proof

Step Hyp Ref Expression
1 frege16 ⊢ ψ → χ → θ → τ → η → ψ → χ → τ → θ → η
2 frege5 ⊢ ψ → χ → θ → τ → η → ψ → χ → τ → θ → η → φ → ψ → χ → θ → τ → η → φ → ψ → χ → τ → θ → η
3 1 2 ax-mp ⊢ φ → ψ → χ → θ → τ → η → φ → ψ → χ → τ → θ → η