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Theorem frege61a 39012
Description: Lemma for frege65a 39016. Proposition 61 of [Frege1879] p. 52. (Contributed by RP, 17-Apr-2020.) (Proof modification is discouraged.)
Assertion
Ref Expression
frege61a ((if-(𝜑, 𝜓, 𝜒) → 𝜃) → ((𝜓𝜒) → 𝜃))

Proof of Theorem frege61a
StepHypRef Expression
1 ax-frege58a 39008 . 2 ((𝜓𝜒) → if-(𝜑, 𝜓, 𝜒))
2 frege9 38945 . 2 (((𝜓𝜒) → if-(𝜑, 𝜓, 𝜒)) → ((if-(𝜑, 𝜓, 𝜒) → 𝜃) → ((𝜓𝜒) → 𝜃)))
31, 2ax-mp 5 1 ((if-(𝜑, 𝜓, 𝜒) → 𝜃) → ((𝜓𝜒) → 𝜃))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 386  if-wif 1089
This theorem was proved from axioms:  ax-mp 5  ax-frege1 38923  ax-frege2 38924  ax-frege8 38942  ax-frege58a 39008
This theorem is referenced by:  frege65a  39016
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