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Theorem frege51 36993
Description: Compare with jaod 393. Proposition 51 of [Frege1879] p. 50. (Contributed by RP, 24-Dec-2019.) (Proof modification is discouraged.)
Assertion
Ref Expression
frege51 ((𝜑 → (𝜓𝜒)) → ((𝜃𝜒) → (𝜑 → ((¬ 𝜓𝜃) → 𝜒))))

Proof of Theorem frege51
StepHypRef Expression
1 frege50 36992 . 2 ((𝜓𝜒) → ((𝜃𝜒) → ((¬ 𝜓𝜃) → 𝜒)))
2 frege18 36956 . 2 (((𝜓𝜒) → ((𝜃𝜒) → ((¬ 𝜓𝜃) → 𝜒))) → ((𝜑 → (𝜓𝜒)) → ((𝜃𝜒) → (𝜑 → ((¬ 𝜓𝜃) → 𝜒)))))
31, 2ax-mp 5 1 ((𝜑 → (𝜓𝜒)) → ((𝜃𝜒) → (𝜑 → ((¬ 𝜓𝜃) → 𝜒))))
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wi 4
This theorem was proved from axioms:  ax-mp 5  ax-frege1 36928  ax-frege2 36929  ax-frege8 36947  ax-frege28 36968  ax-frege31 36972  ax-frege41 36983
This theorem is referenced by:  frege128  37129
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