Metamath Proof Explorer

Theorem frege18

Description: Closed form of a syllogism followed by a swap of antecedents. Proposition 18 of Frege1879 p. 39. (Contributed by RP, 24-Dec-2019) (Proof modification is discouraged.)

Ref Expression
Assertion frege18 ⊢ φ → ψ → χ → θ → φ → ψ → θ → χ

Proof

Step Hyp Ref Expression
1 frege5 ⊢ φ → ψ → χ → θ → φ → θ → ψ → χ
2 frege16 ⊢ φ → ψ → χ → θ → φ → θ → ψ → χ → φ → ψ → χ → θ → φ → ψ → θ → χ
3 1 2 ax-mp ⊢ φ → ψ → χ → θ → φ → ψ → θ → χ