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Theorem frege24 38603
Description: Closed form for a1d 25. Deduction introducing an embedded antecedent. Identical to rp-frege24 38585 which was proved without relying on ax-frege8 38597. Proposition 24 of [Frege1879] p. 42. (Contributed by RP, 24-Dec-2019.) (Proof modification is discouraged.)
Assertion
Ref Expression
frege24 ((𝜑𝜓) → (𝜑 → (𝜒𝜓)))

Proof of Theorem frege24
StepHypRef Expression
1 ax-frege1 38578 . 2 ((𝜑𝜓) → (𝜒 → (𝜑𝜓)))
2 frege12 38601 . 2 (((𝜑𝜓) → (𝜒 → (𝜑𝜓))) → ((𝜑𝜓) → (𝜑 → (𝜒𝜓))))
31, 2ax-mp 5 1 ((𝜑𝜓) → (𝜑 → (𝜒𝜓)))
Colors of variables: wff setvar class
Syntax hints:  wi 4
This theorem was proved from axioms:  ax-mp 5  ax-frege1 38578  ax-frege2 38579  ax-frege8 38597
This theorem is referenced by:  frege25  38605  frege63a  38669  frege63b  38696  frege63c  38714
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