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Theorem rp-8frege 39054
Description: Eliminate antecedent when it is implied by previous antecedent. (Contributed by RP, 24-Dec-2019.)
Assertion
Ref Expression
rp-8frege ((𝜑 → (𝜓 → ((𝜒𝜓) → 𝜃))) → (𝜑 → (𝜓𝜃)))

Proof of Theorem rp-8frege
StepHypRef Expression
1 rp-6frege 39053 . 2 (𝜑 → ((𝜓 → ((𝜒𝜓) → 𝜃)) → (𝜓𝜃)))
2 ax-frege2 39041 . 2 ((𝜑 → ((𝜓 → ((𝜒𝜓) → 𝜃)) → (𝜓𝜃))) → ((𝜑 → (𝜓 → ((𝜒𝜓) → 𝜃))) → (𝜑 → (𝜓𝜃))))
31, 2ax-mp 5 1 ((𝜑 → (𝜓 → ((𝜒𝜓) → 𝜃))) → (𝜑 → (𝜓𝜃)))
Colors of variables: wff setvar class
Syntax hints:  wi 4
This theorem was proved from axioms:  ax-mp 5  ax-frege1 39040  ax-frege2 39041
This theorem is referenced by:  axfrege8  39057
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