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Theorem frege63a 40753
 Description: Proposition 63 of [Frege1879] p. 52. (Contributed by RP, 17-Apr-2020.) (Proof modification is discouraged.)
Assertion
Ref Expression
frege63a (if-(𝜑, 𝜓, 𝜃) → (𝜂 → (((𝜓𝜒) ∧ (𝜃𝜏)) → if-(𝜑, 𝜒, 𝜏))))

Proof of Theorem frege63a
StepHypRef Expression
1 frege62a 40752 . 2 (if-(𝜑, 𝜓, 𝜃) → (((𝜓𝜒) ∧ (𝜃𝜏)) → if-(𝜑, 𝜒, 𝜏)))
2 frege24 40687 . 2 ((if-(𝜑, 𝜓, 𝜃) → (((𝜓𝜒) ∧ (𝜃𝜏)) → if-(𝜑, 𝜒, 𝜏))) → (if-(𝜑, 𝜓, 𝜃) → (𝜂 → (((𝜓𝜒) ∧ (𝜃𝜏)) → if-(𝜑, 𝜒, 𝜏)))))
31, 2ax-mp 5 1 (if-(𝜑, 𝜓, 𝜃) → (𝜂 → (((𝜓𝜒) ∧ (𝜃𝜏)) → if-(𝜑, 𝜒, 𝜏))))
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ∧ wa 399  if-wif 1058 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-frege1 40662  ax-frege2 40663  ax-frege8 40681  ax-frege58a 40747 This theorem depends on definitions:  df-bi 210  df-an 400  df-or 845  df-ifp 1059 This theorem is referenced by: (None)
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