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Theorem frege32 36943
Description: Deduce con1 142 from con3 148. Proposition 32 of [Frege1879] p. 44. (Contributed by RP, 24-Dec-2019.) (Proof modification is discouraged.)
Assertion
Ref Expression
frege32 (((¬ 𝜑𝜓) → (¬ 𝜓 → ¬ ¬ 𝜑)) → ((¬ 𝜑𝜓) → (¬ 𝜓𝜑)))

Proof of Theorem frege32
StepHypRef Expression
1 ax-frege31 36942 . 2 (¬ ¬ 𝜑𝜑)
2 frege7 36916 . 2 ((¬ ¬ 𝜑𝜑) → (((¬ 𝜑𝜓) → (¬ 𝜓 → ¬ ¬ 𝜑)) → ((¬ 𝜑𝜓) → (¬ 𝜓𝜑))))
31, 2ax-mp 5 1 (((¬ 𝜑𝜓) → (¬ 𝜓 → ¬ ¬ 𝜑)) → ((¬ 𝜑𝜓) → (¬ 𝜓𝜑)))
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wi 4
This theorem was proved from axioms:  ax-mp 5  ax-frege1 36898  ax-frege2 36899  ax-frege31 36942
This theorem is referenced by:  frege33  36944
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