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Theorem frege21 38647
Description: Replace antecedent in antecedent. Proposition 21 of [Frege1879] p. 40. (Contributed by RP, 24-Dec-2019.) (Proof modification is discouraged.)
Assertion
Ref Expression
frege21 (((𝜑𝜓) → 𝜒) → ((𝜑𝜃) → ((𝜃𝜓) → 𝜒)))

Proof of Theorem frege21
StepHypRef Expression
1 frege9 38632 . 2 ((𝜑𝜃) → ((𝜃𝜓) → (𝜑𝜓)))
2 frege19 38644 . 2 (((𝜑𝜃) → ((𝜃𝜓) → (𝜑𝜓))) → (((𝜑𝜓) → 𝜒) → ((𝜑𝜃) → ((𝜃𝜓) → 𝜒))))
31, 2ax-mp 5 1 (((𝜑𝜓) → 𝜒) → ((𝜑𝜃) → ((𝜃𝜓) → 𝜒)))
Colors of variables: wff setvar class
Syntax hints:  wi 4
This theorem was proved from axioms:  ax-mp 5  ax-frege1 38610  ax-frege2 38611  ax-frege8 38629
This theorem is referenced by:  frege44  38668  frege47  38671
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