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Theorem frege53a 36977
Description: Lemma for frege55a 36985. Proposition 53 of [Frege1879] p. 50. (Contributed by RP, 24-Dec-2019.) (Proof modification is discouraged.)
Assertion
Ref Expression
frege53a (if-(𝜑, 𝜃, 𝜒) → ((𝜑𝜓) → if-(𝜓, 𝜃, 𝜒)))

Proof of Theorem frege53a
StepHypRef Expression
1 ax-frege52a 36974 . 2 ((𝜑𝜓) → (if-(𝜑, 𝜃, 𝜒) → if-(𝜓, 𝜃, 𝜒)))
2 ax-frege8 36926 . 2 (((𝜑𝜓) → (if-(𝜑, 𝜃, 𝜒) → if-(𝜓, 𝜃, 𝜒))) → (if-(𝜑, 𝜃, 𝜒) → ((𝜑𝜓) → if-(𝜓, 𝜃, 𝜒))))
31, 2ax-mp 5 1 (if-(𝜑, 𝜃, 𝜒) → ((𝜑𝜓) → if-(𝜓, 𝜃, 𝜒)))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wb 194  if-wif 1005
This theorem was proved from axioms:  ax-mp 5  ax-frege8 36926  ax-frege52a 36974
This theorem is referenced by:  frege55a  36985
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