Metamath Proof Explorer

Theorem rp-8frege

Description: Eliminate antecedent when it is implied by previous antecedent. (Contributed by RP, 24-Dec-2019)

Ref Expression
Assertion rp-8frege ⊢ φ → ψ → χ → ψ → θ → φ → ψ → θ

Proof

Step Hyp Ref Expression
1 rp-6frege ⊢ φ → ψ → χ → ψ → θ → ψ → θ
2 ax-frege2 ⊢ φ → ψ → χ → ψ → θ → ψ → θ → φ → ψ → χ → ψ → θ → φ → ψ → θ
3 1 2 ax-mp ⊢ φ → ψ → χ → ψ → θ → φ → ψ → θ