Metamath Proof Explorer

Theorem frege16

Description: A closed form of com34 . Proposition 16 of Frege1879 p. 38. (Contributed by RP, 24-Dec-2019) (Proof modification is discouraged.)

Ref Expression
Assertion frege16 ⊢ φ → ψ → χ → θ → τ → φ → ψ → θ → χ → τ

Proof

Step Hyp Ref Expression
1 frege12 ⊢ ψ → χ → θ → τ → ψ → θ → χ → τ
2 frege5 ⊢ ψ → χ → θ → τ → ψ → θ → χ → τ → φ → ψ → χ → θ → τ → φ → ψ → θ → χ → τ
3 1 2 ax-mp ⊢ φ → ψ → χ → θ → τ → φ → ψ → θ → χ → τ