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Theorem frege61a 41446
Description: Lemma for frege65a 41450. 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 41442 . 2 ((𝜓𝜒) → if-(𝜑, 𝜓, 𝜒))
2 frege9 41379 . 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 396  if-wif 1060
This theorem was proved from axioms:  ax-mp 5  ax-frege1 41357  ax-frege2 41358  ax-frege8 41376  ax-frege58a 41442
This theorem is referenced by:  frege65a  41450
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