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Theorem rp-frege24 40485
Description: Introducing an embedded antecedent. Alternate proof for frege24 40503. Closed form for a1d 25. (Contributed by RP, 24-Dec-2019.)
Assertion
Ref Expression
rp-frege24 ((𝜑𝜓) → (𝜑 → (𝜒𝜓)))

Proof of Theorem rp-frege24
StepHypRef Expression
1 rp-simp2-frege 40480 . 2 (𝜑 → (𝜓 → (𝜒𝜓)))
2 ax-frege2 40479 . 2 ((𝜑 → (𝜓 → (𝜒𝜓))) → ((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 40478  ax-frege2 40479
This theorem is referenced by:  rp-7frege  40489  rp-frege25  40493
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