Metamath Proof Explorer

Theorem frege15

Description: A closed form of com4r . Proposition 15 of Frege1879 p. 38. (Contributed by RP, 24-Dec-2019) (Proof modification is discouraged.)

Ref Expression
Assertion frege15 ⊢ φ → ψ → χ → θ → τ → θ → φ → ψ → χ → τ

Proof

Step Hyp Ref Expression
1 frege14 ⊢ φ → ψ → χ → θ → τ → φ → θ → ψ → χ → τ
2 frege12 ⊢ φ → ψ → χ → θ → τ → φ → θ → ψ → χ → τ → φ → ψ → χ → θ → τ → θ → φ → ψ → χ → τ
3 1 2 ax-mp ⊢ φ → ψ → χ → θ → τ → θ → φ → ψ → χ → τ