Metamath Proof Explorer

Theorem frege14

Description: Closed form of a deduction based on com3r . Proposition 14 of Frege1879 p. 37. (Contributed by RP, 24-Dec-2019) (Proof modification is discouraged.)

Ref Expression
Assertion frege14 ⊢ φ → ψ → χ → θ → τ → φ → θ → ψ → χ → τ

Proof

Step Hyp Ref Expression
1 frege13 ⊢ ψ → χ → θ → τ → θ → ψ → χ → τ
2 frege5 ⊢ ψ → χ → θ → τ → θ → ψ → χ → τ → φ → ψ → χ → θ → τ → φ → θ → ψ → χ → τ
3 1 2 ax-mp ⊢ φ → ψ → χ → θ → τ → φ → θ → ψ → χ → τ