Metamath Proof Explorer

Theorem frege7

Description: A closed form of syl6 . The first antecedent is used to replace the consequent of the second antecedent. Proposition 7 of Frege1879 p. 34. (Contributed by RP, 24-Dec-2019) (Proof modification is discouraged.)

Ref Expression
Assertion frege7 ⊢ φ → ψ → χ → θ → φ → χ → θ → ψ

Proof

Step Hyp Ref Expression
1 frege5 ⊢ φ → ψ → θ → φ → θ → ψ
2 frege6 ⊢ φ → ψ → θ → φ → θ → ψ → φ → ψ → χ → θ → φ → χ → θ → ψ
3 1 2 ax-mp ⊢ φ → ψ → χ → θ → φ → χ → θ → ψ