Metamath Proof Explorer

Theorem rp-7frege

Description: Distribute antecedent and add another. (Contributed by RP, 24-Dec-2019)

Ref Expression
Assertion rp-7frege ⊢ φ → ψ → χ → θ → φ → ψ → φ → χ

Proof

Step Hyp Ref Expression
1 ax-frege2 ⊢ φ → ψ → χ → φ → ψ → φ → χ
2 rp-frege24 ⊢ φ → ψ → χ → φ → ψ → φ → χ → φ → ψ → χ → θ → φ → ψ → φ → χ
3 1 2 ax-mp ⊢ φ → ψ → χ → θ → φ → ψ → φ → χ