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Theorem rp-frege3g 39509
 Description: Add antecedent to ax-frege2 39506. More general statement than frege3 39510. Like ax-frege2 39506, it is essentially a closed form of mpd 15, however it has an extra antecedent. It would be more natural to prove from a1i 11 and ax-frege2 39506 in Metamath. (Contributed by RP, 24-Dec-2019.) (Proof modification is discouraged.)
Assertion
Ref Expression
rp-frege3g (𝜑 → ((𝜓 → (𝜒𝜃)) → ((𝜓𝜒) → (𝜓𝜃))))

Proof of Theorem rp-frege3g
StepHypRef Expression
1 ax-frege2 39506 . 2 ((𝜓 → (𝜒𝜃)) → ((𝜓𝜒) → (𝜓𝜃)))
2 ax-frege1 39505 . 2 (((𝜓 → (𝜒𝜃)) → ((𝜓𝜒) → (𝜓𝜃))) → (𝜑 → ((𝜓 → (𝜒𝜃)) → ((𝜓𝜒) → (𝜓𝜃)))))
31, 2ax-mp 5 1 (𝜑 → ((𝜓 → (𝜒𝜃)) → ((𝜓𝜒) → (𝜓𝜃))))
 Colors of variables: wff setvar class Syntax hints:   → wi 4 This theorem was proved from axioms:  ax-mp 5  ax-frege1 39505  ax-frege2 39506 This theorem is referenced by:  rp-frege4g  39513
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