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Theorem frege45 40073
Description: Deduce pm2.6 192 from con1 148. Proposition 45 of [Frege1879] p. 47. (Contributed by RP, 24-Dec-2019.) (Proof modification is discouraged.)
Assertion
Ref Expression
frege45 (((¬ 𝜑𝜓) → (¬ 𝜓𝜑)) → ((¬ 𝜑𝜓) → ((𝜑𝜓) → 𝜓)))

Proof of Theorem frege45
StepHypRef Expression
1 frege44 40072 . 2 ((¬ 𝜓𝜑) → ((𝜑𝜓) → 𝜓))
2 frege5 40024 . 2 (((¬ 𝜓𝜑) → ((𝜑𝜓) → 𝜓)) → (((¬ 𝜑𝜓) → (¬ 𝜓𝜑)) → ((¬ 𝜑𝜓) → ((𝜑𝜓) → 𝜓))))
31, 2ax-mp 5 1 (((¬ 𝜑𝜓) → (¬ 𝜓𝜑)) → ((¬ 𝜑𝜓) → ((𝜑𝜓) → 𝜓)))
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wi 4
This theorem was proved from axioms:  ax-mp 5  ax-frege1 40014  ax-frege2 40015  ax-frege8 40033  ax-frege28 40054  ax-frege31 40058  ax-frege41 40069
This theorem is referenced by:  frege46  40074
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