Metamath Proof Explorer

Theorem frege17

Description: A closed form of com3l . Proposition 17 of Frege1879 p. 39. (Contributed by RP, 24-Dec-2019) (Proof modification is discouraged.)

Ref Expression
Assertion frege17 ⊢ φ → ψ → χ → θ → ψ → χ → φ → θ

Proof

Step Hyp Ref Expression
1 ax-frege8 ⊢ φ → ψ → χ → θ → ψ → φ → χ → θ
2 frege16 ⊢ φ → ψ → χ → θ → ψ → φ → χ → θ → φ → ψ → χ → θ → ψ → χ → φ → θ
3 1 2 ax-mp ⊢ φ → ψ → χ → θ → ψ → χ → φ → θ