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