Metamath Proof Explorer

Theorem frege13

Description: A closed form of com3r . Proposition 13 of Frege1879 p. 37. (Contributed by RP, 24-Dec-2019) (Proof modification is discouraged.)

Ref Expression
Assertion frege13 ⊢ φ → ψ → χ → θ → χ → φ → ψ → θ

Proof

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