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Theorem frege24 40514
Description: Closed form for a1d 25. Deduction introducing an embedded antecedent. Identical to rp-frege24 40496 which was proved without relying on ax-frege8 40508. 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 40489 . 2 ((𝜑𝜓) → (𝜒 → (𝜑𝜓)))
2 frege12 40512 . 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 40489  ax-frege2 40490  ax-frege8 40508
This theorem is referenced by:  frege25  40516  frege63a  40580  frege63b  40607  frege63c  40625
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